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Abstract: In 1.9 of the paper [A. Hahn, A Hermitian Morita theorem for algebras with anti-structure, J. Algebra 93 (1985) 215–235], should be replaced by . This leads to minor changes in the rest of the paper where the ring should be replaced by its opposite and vice versa. [Copyright &y& Elsevier]

The goal of this paper is to study primitive groups that are contained in the union of maximal (in the symmetric group) imprimitive groups. The study of types of permutations that appear inside primitive groups goes back to the origins of the theory of permutation groups. However, this is another instance of a situation common in mathematics in which a very natural problem turns out to be extremely difficult. Fortunately, the enormous progresses of the last few decades seem to allow a new momentum on the attack to this problem. In this paper we prove that there are infinite families of primitive groups contained in the union of imprimitive groups and propose a new hierarchy for primitive groups based on that fact. In addition we introduce some algorithms to handle permutations, provide the corresponding GAP implementation, solve some open problems, and propose a large list of open problems. [ABSTRACT FROM AUTHOR]

Let G be a finite group of Lie type defined in characteristic p , and let k be an algebraically closed field of characteristic r > 0. We will assume that r ≠ p (so, we are in the non-defining characteristic case). Let V be a finite-dimensional irreducible left kG -module. In 2011, Guralnick and Tiep found bounds on the dimension of H 1 (G , V) in non-defining characteristic, which are independent of V. The aim of this paper is to generalize the work of Gurlanick and Tiep. We assume that G is split and use methods of modular Harish-Chandra theory to find bounds on the dimension of Ext k G 1 (Y , V) , where Y and V are irreducible kG -modules. We then use Dipper and Du's algorithms to illustrate our bounds in a series of examples. [ABSTRACT FROM AUTHOR]

In this paper we construct HNN-extensions of diassociative algebras and Leibniz algebras and prove that every Leibniz algebra embeds into any of its HNN-extensions. We also prove that every Leibniz algebra with at most countable dimension embeds into a two-generator Leibniz algebra. [ABSTRACT FROM AUTHOR]

Abstract Triangular decomposition is one of the standard ways to represent the radical of a polynomial ideal. A general algorithm for computing such a decomposition was proposed by A. Szántó. In this paper, we give the first complete bounds for the degrees of the polynomials and the number of components in the output of the algorithm, providing explicit formulas for these bounds. [ABSTRACT FROM AUTHOR]

Abstract In this paper we consider several classical and novel algorithmic problems for right-angled Artin groups, some of which are closely related to graph theoretic problems, and study their computational complexity. We study these problems with a view towards applications to cryptography. [ABSTRACT FROM AUTHOR]

A proper subsemigroup of a semigroup is maximal if it is not contained in any other proper subsemigroup. A maximal subsemigroup of a finite semigroup has one of a small number of forms, as described in a paper of Graham, Graham, and Rhodes. Determining which of these forms arise in a given finite semigroup is difficult, and no practical mechanism for doing so appears in the literature. We present an algorithm for computing the maximal subsemigroups of a finite semigroup S given knowledge of the Green's structure of S , and the ability to determine maximal subgroups of certain subgroups of S , namely its group H -classes. In the case of a finite semigroup S represented by a generating set X , in many examples, if it is practical to compute the Green's structure of S from X , then it is also practical to find the maximal subsemigroups of S using the algorithm we present. In such examples, the time taken to determine the Green's structure of S is comparable to that taken to find the maximal subsemigroups. The generating set X for S may consist, for example, of transformations, or partial permutations, of a finite set, or of matrices over a semiring. Algorithms for computing the Green's structure of S from X include the Froidure–Pin Algorithm, and an algorithm of the second author based on the Schreier–Sims algorithm for permutation groups. The worst case complexity of these algorithms is polynomial in | S | , which for, say, transformation semigroups is exponential in the number of points on which they act. Certain aspects of the problem of finding maximal subsemigroups reduce to other well-known computational problems, such as finding all maximal cliques in a graph and computing the maximal subgroups in a group. The algorithm presented comprises two parts. One part relates to computing the maximal subsemigroups of a special class of semigroups, known as Rees 0-matrix semigroups. The other part involves a careful analysis of certain graphs associated to the semigroup S , which, roughly speaking, capture the essential information about the action of S on its J -classes. [ABSTRACT FROM AUTHOR]

In this paper, a new algorithm is presented for deciding the semi-definiteness of multivariate polynomials with coefficients in a computable ordered field, which admits an effective method of finding an isolating set for every non-zero univariate polynomial. This algorithm is an improvement of the method presented in Ref. [24]. The technique in this paper is to compute triangular decompositions of polynomial systems into regular chains. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the Peskine version of Zariski Main Theorem published in 1965 and discusses some applications. It is written in the style of Bishop's constructive mathematics. Being constructive, each proof in this paper can be interpreted as an algorithm for constructing explicitly the conclusion from the hypothesis. The main non-constructive argument in the proof of Peskine is the use of minimal prime ideals. Essentially we substitute this point by two dynamical arguments; one about gcd's, using subresultants, and another using our notion of strong transcendence. In particular we obtain algorithmic versions for the Multivariate Hensel Lemma and the structure theorem of quasi-finite algebras. [Copyright &y& Elsevier]

Let g be a finite-dimensional semisimple Lie algebra over C having rank l and let V be an irreducible finite-dimensional g -module having highest weight λ . Computations of weight multiplicities in V , usually based on Freudenthal's formula, are in general difficult to carry out in large ranks or for λ with large coefficients (in terms of the fundamental weights). In this paper, we first show that in some situations, these coefficients can be “lowered” in order to simplify the calculations. We then investigate how this can be used to improve the aforementioned formula of Freudenthal, leading to a more efficient version of the latter in terms of complexity as well as to a way of dealing with certain computations in unbounded ranks. We conclude by illustrating the last assertion with a concrete example. [ABSTRACT FROM AUTHOR]

Babai and Pak proved that the product replacement algorithm (a widely used heuristic algorithm intended to rapidly generate nearly uniformly distributed random elements in a finite group G ) has a flaw. Indeed the projection of the uniform distribution on generating n -tuples onto the first component may not give the uniform distribution on elements of G . In this paper we examine the difference between this distribution and the uniform one, in the particular case when G is a finitely generated prosoluble group. Under some additional hypotheses (for example if the derived subgroup is pronilpotent), this bias is bounded away from 1. However even for soluble groups, the problem pointed out by Babai and Pak is unavoidable. We construct a sequence of finite soluble groups of derived length 4 for which the bias is close to 1. [ABSTRACT FROM AUTHOR]

This paper studies decision problems for semigroups that are word-hyperbolic in the sense of Duncan and Gilman. A fundamental investigation reveals that the natural definition of a ‘word-hyperbolic structure’ has to be strengthened slightly in order to define a unique semigroup up to isomorphism. (This does not alter the class of word-hyperbolic semigroups.) The isomorphism problem is proven to be undecidable for word-hyperbolic semigroups (in contrast to the situation for word-hyperbolic groups). It is proved that it is undecidable whether a word-hyperbolic semigroup is automatic, asynchronously automatic, biautomatic, or asynchronously biautomatic. (These properties do not hold in general for word-hyperbolic semigroups.) It is proved that the uniform word problem for word-hyperbolic semigroups is solvable in polynomial time (improving on the previous exponential-time algorithm). Algorithms are presented for deciding whether a word-hyperbolic semigroup is a monoid, a group, a completely simple semigroup, a Clifford semigroup, or a free semigroup. [ABSTRACT FROM AUTHOR]

A threefold isogenous to a product of curves X is a quotient of a product of three compact Riemann surfaces of genus at least two by the free action of a finite group. In this paper we study these threefolds under the assumption that the group acts diagonally on the product. We show that the classification of these threefolds is a finite problem, present an algorithm to classify them for a fixed value of χ ( O X ) and explain a method to determine their Hodge numbers. Running an implementation of the algorithm we achieve the full classification of threefolds isogenous to a product of curves with χ ( O X ) = − 1 , under the assumption that the group acts faithfully on each factor. [ABSTRACT FROM AUTHOR]

Let A be a basic and connected finite dimensional algebra and D b ( A ) be the bounded derived category of finitely generated left A -modules. In this paper we consider lengths of tilting objects and indecomposable compact exceptional objects in D b ( A ) , and prove a sufficient condition such that these lengths are bounded by the number of isomorphism classes of simple A -modules. Moreover, we show that algebras satisfying this criterion are bounded derived simple, and describe an algorithm to construct a family of algebras satisfying this condition. [ABSTRACT FROM AUTHOR]

In this paper, we consider the open question: is the cortex of the dual of a nilpotent Lie algebra an algebraic set? We give a partial answer by considering the class of two-step nilpotent Lie algebra g . For this class of Lie algebras we give an explicit algorithm for finding its corresponding cortex. By the way, we prove that either the cortex coincides with the zero set of invariant homogeneous polynomials and in this case is z ⊥ where z denotes the center of g , or it is a proper projective algebraic subset of z ⊥ . Finally we materialize our algorithm on examples. [ABSTRACT FROM AUTHOR]

For a p -group P , p a prime, there are two versions of the Thompson subgroup of P , namely the elementary version J e ( P ) and the non-elementary version J ( P ) . This paper describes algorithms for calculating these two subgroups. Depending on P , these algorithms are effective for groups of order up to p 30 . By modifying these algorithms we also produce algorithms for K ( P ) , a further characteristic subgroup also introduced by Thompson [20] , and characteristic subgroups D ( P ) and D e ( P ) introduced by Glauberman and Solomon [12] . Sample calculations using these algorithms are discussed with an accompanying file giving details of these calculations, along with the code for the algorithm. [ABSTRACT FROM AUTHOR]

Abstract: The Bernstein–Sato polynomial of a hypersurface is an important object with many applications. However, its computation is hard, as a number of open questions and challenges indicate. In this paper we propose a family of algorithms called checkRoot for optimized checking whether a given rational number is a root of Bernstein–Sato polynomial and in the affirmative case, computing its multiplicity. These algorithms are used in the new approach to compute the global or local Bernstein–Sato polynomial and b-function of a holonomic ideal with respect to a weight vector. They can be applied in numerous situations, where a multiple of the Bernstein–Sato polynomial can be established. Namely, a multiple can be obtained by means of embedded resolution, for topologically equivalent singularities or using the formula of AʼCampo and spectral numbers. We also present approaches to the logarithmic comparison problem and the intersection homology D-module. Several applications are presented as well as solutions to some challenges which were intractable with the classical methods. One of the main applications is the computation of a stratification of affine space with the local b-function being constant on each stratum. Notably, the algorithm we propose does not employ primary decomposition. Our results can be also applied for the computation of Bernstein–Sato polynomials for varieties. The examples in the paper have been computed with our implementation of the methods described in Singular:Plural. [Copyright &y& Elsevier]

Abstract: Quasimodules for vertex algebras are generalizations of modules for vertex algebras. These new objects arise from a generalization of locality for fields. Quasimodules tie together module theory and twisted module theory, and both twisted and untwisted modules feature Poincaré–Birkhoff–Witt-like spanning sets. This paper generalizes these spanning set results to quasimodules for certain Möbius vertex algebras. In particular this paper presents two spanning sets, one featuring a difference-zero ordering restriction on modes and another featuring a difference-one ordering restriction. [Copyright &y& Elsevier]

Abstract: An element in Artin''s braid group is said to be periodic if some power of it lies in the center of . In this paper we prove that all previously known algorithms for solving the conjugacy search problem in are exponential in the braid index n for the special case of periodic braids. We overcome this difficulty by putting to work several known isomorphisms between Garside structures in the braid group and other Garside groups. This allows us to obtain a polynomial solution to the original problem in the spirit of the previously known algorithms. This paper is the third in a series of papers by the same authors about the conjugacy problem in Garside groups. They have a unified goal: the development of a polynomial algorithm for the conjugacy decision and search problems in , which generalizes to other Garside groups whenever possible. It is our hope that the methods introduced here will allow the generalization of the results in this paper to all Artin–Tits groups of spherical type. [Copyright &y& Elsevier]

Algorithms to decide isomorphism of modules have been honed continually over the last 30 years, and their range of applicability has been extended to include modules over a wide range of rings. Highly efficient computer implementations of these algorithms form the bedrock of systems such as GAP and Magma , at least in regard to computations with groups and algebras. By contrast, the fundamental problem of testing for isomorphism between other types of algebraic structures – such as groups, and almost any type of algebra – seems today as intractable as ever. What explains the vastly different complexity status of the module isomorphism problem? This paper argues that the apparent discrepancy is explained by nomenclature. Current algorithms to solve module isomorphism, while efficient and immensely useful, are actually solving a highly constrained version of the problem. We report that module isomorphism in its general form is as hard as algebra isomorphism and graph isomorphism, both well-studied problems that are widely regarded as difficult. On a more positive note, for cyclic rings we describe a polynomial-time algorithm for the general module isomorphism problem. We also report on a Magma implementation of our algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate certain deformations of the negative part of quantized enveloping algebras . An algorithm is established to determine when a given is a PBW-deformation of . For of type and , we classify PBW-deformations of . Moreover, we explicitly construct some PBW bases for a class of PBW-deformations of . As an application, Iorgov–Klimyk's PBW bases for the non-standard quantum deformation of the universal enveloping algebra are recovered. [Copyright &y& Elsevier]

Abstract: Let k be any field of characteristic not equaling 2. Djoković showed that every anisotropic -lattice has a reduced basis which enabled Gerstein to complete the classification of definite -lattices. This paper extends Djokovićʼs reduction algorithm to include the isotropic case. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to outline the structure of the category of the Gorenstein projective Λ-modules, where Λ is a Nakayama algebra. In addition, we are going to introduce the resolution quiver of Λ. It provides a fast algorithm in order to obtain the Gorenstein projective Λ-modules and to decide whether Λ is a Gorenstein algebra or not, and whether it is CM-free or not. [Copyright &y& Elsevier]

Abstract: In the paper we derive a Gröbner–Shirshov algorithm for semirings and commutative semirings. As applications, we obtain Gröbner–Shirshov bases and A. Blassʼs (1995) and M. Fiore and T. Leinsterʼs (2004) normal forms of the semirings and , correspondingly. [Copyright &y& Elsevier]

Abstract: We describe an algorithm for obtaining generators of the unit group of the integral group ring of a finite abelian group G. We used our implementation in Magma of this algorithm to compute the unit groups of for G of order up to 110. In particular for those cases we obtained the index of the group of Hoechsmann units in the full unit group. At the end of the paper we describe an algorithm for the more general problem of finding generators of an arithmetic group corresponding to a diagonalisable algebraic group. [Copyright &y& Elsevier]

Abstract: In Howlett and Nguyen (2010) , the concept of a W-graph ideal in a Coxeter group was introduced, and it was shown how a W-graph can be constructed from a given W-graph ideal. In this paper, we describe a class of W-graph ideals from which certain Kazhdan–Lusztig left cells arise. The result justifies the algorithm as illustrated in Howlett and Nguyen (2010) for the construction of W-graphs for Specht modules for the Hecke algebra of type A. [Copyright &y& Elsevier]

Abstract: We introduce a concept of a W-graph ideal in a Coxeter group. The main goal of this paper is to describe how to construct a W-graph from a given W-graph ideal. The principal application of this idea is in type A, where it provides an algorithm for the construction of W-graphs for Specht modules. [Copyright &y& Elsevier]

Abstract: The Lazard correspondence establishes an equivalence of categories between p-groups of nilpotency class less than p and nilpotent Lie rings of the same class and order. The main tools used to achieve this are the Baker–Campbell–Hausdorff formula and its inverse formulae. Here we describe methods to compute the inverse Baker–Campbell–Hausdorff formulae. Using these we get an algorithm to compute the Lie ring structure of a p-group of class

Abstract: This paper is devoted to understanding the defining ideal of a Nichols algebra from the decomposition of specific elements in the group algebra of braid groups. A family of primitive elements is found and algorithms are proposed. To prove the main result, the differential algebra of a Nichols algebra is constructed. Moreover, another point of view on Serre relations is provided. [Copyright &y& Elsevier]

Abstract: In this paper we give an explicit algorithm to construct the ordinary quiver of a finite EI category for which the endomorphism groups of all objects have orders invertible in the field k. We classify all finite EI categories with hereditary category algebras, characterizing them as free EI categories (in a sense which we define) for which all endomorphism groups of objects have invertible orders. Some applications on the representation types of finite EI categories are derived. [Copyright &y& Elsevier]

Abstract: In this paper, we describe an algorithm to compute modular correspondences in the coordinate system provided by the theta null points of abelian varieties together with a theta structure. As an application, this algorithm can be used to speed up the initialization phase of a point counting algorithm (Carls and Lubicz, 2008 ). The main part of the algorithm is the resolution of an algebraic system for which we have designed a specialized Gröbner basis algorithm. Our algorithm takes advantage of the structure of the algebraic system in order to speed up the resolution. We remark that this special structure comes from the action of the automorphisms of the theta group on the solutions of the system which has a nice geometric interpretation. In particular we were able to count the solutions of the system and to identify which ones correspond to valid theta null points. [Copyright &y& Elsevier]

Abstract: In this paper we complete the classification of right coideal subalgebras containing all grouplike elements for the multiparameter version of the quantum group , . It is known that every such subalgebra has a triangular decomposition , where and are right coideal subalgebras of negative and positive quantum Borel subalgebras. We found a necessary and sufficient condition for the above triangular composition to be a right coideal subalgebra of in terms of the PBW-generators of the components. Furthermore, an algorithm is given that allows one to find an explicit form of the generators. Using a computer realization of that algorithm, we determined the number of different right coideal subalgebras that contain all grouplike elements for . If q has a finite multiplicative order , the classification remains valid for homogeneous right coideal subalgebras of the multiparameter version of the Lusztig quantum group (the Frobenius–Lusztig kernel of type ) in which case the total number of homogeneous right coideal subalgebras and the particular generators are the same. [Copyright &y& Elsevier]

Abstract: In this paper we establish a Gröbner–Shirshov bases theory for Lie algebras over commutative rings. As applications we give some new examples of special Lie algebras (those embeddable in associative algebras over the same ring) and non-special Lie algebras (following a suggestion of P.M. Cohn (1963) ). In particular, Cohnʼs Lie algebras over the characteristic p are non-special when . We present an algorithm that one can check for any p, whether Cohnʼs Lie algebras are non-special. Also we prove that any finitely or countably generated Lie algebra is embeddable in a two-generated Lie algebra. [Copyright &y& Elsevier]

Abstract: We take a graph theoretic approach to the problem of finding generators for those prime ideals of which are invariant under the torus action . Launois (2004) has shown that the generators consist of certain quantum minors of the matrix of canonical generators of and in Launois (2004) gives an algorithm to find them. In this paper we modify a classic result of Lindström (1973) and Gessel and Viennot (1985) to show that a quantum minor is in the generating set for a particular ideal if and only if we can find a particular set of vertex-disjoint directed paths in an associated directed graph. [Copyright &y& Elsevier]

Abstract: In the first part of this paper we study scrollers and linearly joined varieties. Scrollers were introduced in Barile and Morales (2004) , linearly joined varieties are an extension of scrollers and were defined in Eisenbud et al. (2005) , there they proved that scrollers are defined by homogeneous ideals having a 2-linear resolution. A particular class of varieties, of important interest in classical Geometry are Cohen–Macaulay varieties of minimal degree, they were classified geometrically by the successive contribution of Del Pezzo (1885) , Bertini (1907) , and Xambo (1981) and algebraically in Barile and Morales (2000) . They appear naturally studying the fiber cone of a codimension two toric ideals Morales (1995) , Gimenez et al. (1993, 1999) , Barile and Morales (1998) , Ha (2006) , Ha and Morales (2009) . Let S be a polynomial ring and a homogeneous ideal defining a sequence of linearly joined varieties. [•] We compute . [•] We prove that , where is the connectedness dimension of the algebraic set defined by . [•] We characterize sets of generators of , and give an effective algorithm to find equations, as an application we prove that in the case where is a union of linear spaces, in particular this applies to any square free monomial ideal having a 2-linear resolution. [•] In the case where is a union of linear spaces, the ideal can be characterized by a tableau, which is an extension of a Ferrer (or Young) tableau. All these results are new, and extend results in Barile and Morales (2004) , Eisenbud et al. (2005) . [Copyright &y& Elsevier]

Abstract: This paper provides a simplified presentation of a known algorithm for resolution of singularities (in characteristic zero). It works in the context of marked ideals and uses naturality properties with respect to open restrictions and strong equivalence, to solve a delicate glueing problem that arises when induction on the dimension of the objects considered is applied. [ABSTRACT FROM AUTHOR]

Abstract: Normaliz is a program for the computation of Hilbert bases of rational cones and the normalizations of affine monoids. It may also be used for solving diophantine linear systems. In this paper we present the algorithms implemented in the program. [Copyright &y& Elsevier]

Abstract: Zariski chambers provide a natural decomposition of the big cone of an algebraic surface into rational locally polyhedral subcones that are interesting from the point of view of linear series. In the present paper we present an algorithm that allows to effectively determine Zariski chambers when the negative curves on the surface are known. We show how the algorithm can be used to compute the number of chambers on Del Pezzo surfaces. [Copyright &y& Elsevier]

Abstract: In this paper, we study the combinatorics related to complements of tableaux. Using the representation theory of general linear groups and a known construction of the dual Weyl modules, we obtain a new straightening algorithm for bideterminants and prove that it is compatible with the complement construction of tableaux. As an application, we get a purely combinatorial construction of the isomorphisms between generalized (classical) Schur algebras introduced first by Henke, Koenig and the author. [Copyright &y& Elsevier]

Abstract: This paper discusses the decomposition of representations of finite groups in characteristic zero, with special emphasis on homogeneous modules. An improved method to compute the endomorphism ring of a representation is presented and a novel algorithm to find singular elements in the endomorphism ring is given. Several explicit examples illustrate the practicality and scope of the various techniques. [Copyright &y& Elsevier]

Abstract: The paper develops algorithmic methods to enumerate all normal subgroups of a finitely presented group such that the factor groups are either isomorphic to or to . The case of two generators is treated in detail. A range of examples starting with the free group on two generators and ending with groups having only finitely many normal subgroups of this type is discussed. [Copyright &y& Elsevier]

Abstract: Let L be the Lie algebra of a simple algebraic group defined over a field and let H be a split maximal toral subalgebra of L. Then L has a Chevalley basis with respect to H. If , it is known how to find it. In this paper, we treat the remaining two characteristics. To this end, we present a few new methods, implemented in Magma, which vary from the computation of centralizers of one root space in another to the computation of a specific part of the Lie algebra of derivations of L. [Copyright &y& Elsevier]

Abstract: In this paper, we obtain Gröbner–Shirshov (non-commutative Gröbner) bases for braid groups in the Birman–Ko–Lee generators enriched by “Garside word”δ [J. Birman, K.H. Ko, S.J. Lee, A new approach to the word and conjugacy problems for the braid groups, Adv. Math. 139 (1998) 322–353]. It gives a new algorithm for getting the Birman–Ko–Lee normal forms in braid groups, and thus a new algorithm for solving the word problem in these groups. [Copyright &y& Elsevier]

Abstract: Let be a free group of rank n generated by . In this paper we discuss three algorithmic problems related to automorphisms of . A word of is called positive if no negative exponents of occur in u. A word u in is called potentially positive if is positive for some automorphism ϕ of . We prove that there is an algorithm to decide whether or not a given word in is potentially positive, which gives an affirmative solution to problem F34a in [G. Baumslag, A.G. Myasnikov, V. Shpilrain, Open problems in combinatorial group theory, second ed., in: Contemp. Math., vol. 296, 2002, pp. 1–38, online version: http://www.grouptheory.info] for the case of . Two elements u and v in are said to be boundedly translation equivalent if the ratio of the cyclic lengths of and is bounded away from 0 and from ∞ for every automorphism ϕ of . We provide an algorithm to determine whether or not two given elements of are boundedly translation equivalent, thus answering question F38c in the online version of [G. Baumslag, A.G. Myasnikov, V. Shpilrain, Open problems in combinatorial group theory, second ed., in: Contemp. Math., vol. 296, 2002, pp. 1–38, online version: http://www.grouptheory.info] for the case of . We also provide an algorithm to decide whether or not a given finitely generated subgroup of is the fixed point group of some automorphism of , which settles problem F1b in [G. Baumslag, A.G. Myasnikov, V. Shpilrain, Open problems in combinatorial group theory, second ed., in: Contemp. Math., vol. 296, 2002, pp. 1–38, online version: http://www.grouptheory.info] in the affirmative for the case of . [Copyright &y& Elsevier]

Abstract: In this paper we classify irreducible, admissible representations of p-adic classical groups in a purely algebraic way. We present a new and simple algorithm for constructing the classifying data which is also useful in other contexts where the computation with Jacquet modules or constant terms of Eisenstein series appears. We construct and study non-standard intertwining operators. They are defined in a purely algebraic way although their rationality follows from [G. Muić, A geometric construction of intertwining operators for reductive p-adic groups, Manuscripta Math. 125 (2008) 241–272]. [Copyright &y& Elsevier]

Abstract: In this paper we consider partial actions of groups on algebras and partial skew group rings. After some general results we prove two versions of Maschke''s theorem and then we study von Neumann regularity, the prime radical and the Jacobson radical of partial skew group rings. In this way we extend many results which are known for skew group rings. [Copyright &y& Elsevier]

Abstract: In this paper, we study the structure of an assosymmetric algebra A by investigating various radicals and show that the Wedderburn principal theorem holds when has no 1-dimensional factor where is the radical of A and also discuss a Pierce decomposition of A. [Copyright &y& Elsevier]

Abstract: We study the relation between certain increasing and decreasing subsequences occurring in the row form of certain elements in the symmetric group, following Schensted [C. Schensted, Longest increasing and decreasing subsequences, Canad. J. Math. 13 (1961) 179–191] and Greene [C. Greene, An extension of Schensted''s theorem, Adv. Math. 14 (1974) 254–265], and the Kazhdan–Lusztig cells [D.A. Kazhdan, G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979) 165–184] of the symmetric group to which they belong. We show that, in the two-sided cell corresponding to a partition λ, there is an explicitly defined element , each of whose prefixes can be used to obtain a left cell by multiplying the cell containing the longest element of the parabolic subgroup associated with λ on the right. Furthermore, we show that the elements of these left cells are those which possess increasing and decreasing subsequences of certain types. The results in this paper lead to efficient algorithms for the explicit descriptions of many left cells inside a given two-sided cell, and the authors have implemented these algorithms in GAP. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a generalization for the class of laura algebras, called almost laura. We show that this new class of algebras retains most of the essential features of laura algebras, especially concerning the important role played by the non-semiregular components in their Auslander–Reiten quivers. Also, we study more intensively the left supported almost laura algebras, showing that these are characterized by the presence of a generalized standard, convex and faithful component. Finally, we prove that almost laura algebras behave well with respect to full subcategories, split-by-nilpotent extensions and skew group algebras. [Copyright &y& Elsevier]

Abstract: In [M. Dettweiler, S. Reiter, An algorithm of Katz and its application to the inverse Galois problem, J. Symbolic Comput. 30 (2000) 761–798], a purely algebraic analogon of Katz'' middle convolution functor (see [N.M. Katz, Rigid Local Systems, Ann. of Math. Stud., vol. 139, Princeton University Press, 1997]) is given. In this paper, we find an explicit Riemann–Hilbert correspondence for this functor. This leads to a construction algorithm for differential systems which correspond to rigid local systems on the punctured affine line via the Riemann–Hilbert correspondence. [Copyright &y& Elsevier]