Search

Let G be a simply connected semisimple algebraic groups over ℂ and let ρ:G→GL(Vλ) be an irreducible representation of G of highest weight λ. Suppose that ρ has finite kernel. Springer defined an adjoint-invariant regular map with Zariski dense image from the group to the Lie algebra, 휃λ:G→픤, which depends on λ. This map, 휃λ, takes the maximal torus T of G to its Lie algebra 픱. Thus, for a given simple group G and an irreducible representation Vλ, one may write , where we take the simple coroots as a basis for 픱. We give a complete determination for these coefficients ci(t) for any simple group G as a sum over the weights of the torus action on Vλ. [ABSTRACT FROM AUTHOR]

In this paper, we present the categories associated to the square matrix with coefficients 2 of order 3. The family of categories associated to these matrices has five isomorphism classes. In the case of a matrix of order higher than 3, we only demonstrate upper and lower bounds for the number of associated categories. [ABSTRACT FROM AUTHOR]

Let (R,𝔪) be a local ring andIan ideal. The aim of the present paper is twofold. At first we continue the investigation to comparefgrade(I,R) withdepth R∕Iand further we derive some results on the vanishing of Lyubeznik numbers. [ABSTRACT FROM PUBLISHER]

We state and prove a fusion system version of Mislin’s theorem [9] on cohomology and control of fusion using Mackey functors. The issue of an algebraic proof is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, poor abelian groups are characterized. It is proved that an abelian group is poor if and only if its torsion part contains a direct summand isomorphic to, wherePis the set of prime integers. We also prove that pi-poor abelian groups exist. Namely, it is proved that the direct sum ofU(ℕ), whereUranges over all nonisomorphic uniform abelian groups, is pi-poor. Moreover, for a pi-poor abelian groupM, it is shown thatMcan not be torsion, and eachp-primary component ofMis unbounded. Finally, we show that there are pi-poor groups which are not poor, and vise versa. [ABSTRACT FROM AUTHOR]

A ring is of finite type if it has only finitely many maximal right ideals, all two-sided. In this article, we give a complete set of invariants for finite direct sums of cyclically presented modules over a ring R of finite type. More generally, our results apply to finite direct sums of direct summands of cyclically presented right R-modules (DCP modules). Using a duality, we obtain as an application a similar set of invariants for kernels of morphisms between finite direct sums of pair-wise non-isomorphic indecomposable injective modules over an arbitrary ring. This application motivates the study of DCP modules. [ABSTRACT FROM AUTHOR]

Tom Dieck introduced a commutative triangle whereby the exponential morphism from the Burnside functor to the unit functor is factorized through the real representation functor. Tornehave introduced a p-adic variant of the exponential morphism. His construction involves real representations that are not well defined up to isomorphism. To obtain a well defined commutative triangle, we introduce the orientation functor, a quotient of the real representation functor. [ABSTRACT FROM AUTHOR]

For a class L of right modules we investigate the relations of monomorphic L-envelopes and epimorphic L-covers over pullback-pushout diagrams, and obtain some isomorphism equations between the envelopes of covers and the covers of envelopes. [ABSTRACT FROM AUTHOR]

Tue study of coset monoids was initiated by Schein in 1966. The coset monoid of a group G, denoted ...(G), consists of all cosets of all subgroups of G. We show how to generalize ...(G) by constructing a monoid ...ℒ(G) of cosets of subgroups from a semilattice (ℒ, ∨ℒ) of subgroups of G which satisfies certain conditions. When (ℒ, ∨ℒ) = (...(G), ∨) is the join semilattice of all subgroups of G , we recover the coset monoid ...(G). The class of semigroups which are isomorphic to some ...ℒ(G) has a very simple description. Elements of the monoids in this class may be represented by cosets of subgroups of their group of units. We show that the factorizable part of the symmetric (resp. dual symmetric) inverse semigroup does not (resp. does) belong to this class. [ABSTRACT FROM AUTHOR]

In this paper we classify, up to exact isomorphism, the algebras in the title which contain a faithful element and in which every non-trivial table subset has dimension at least five. [ABSTRACT FROM AUTHOR]

Let D be a Prüfer domain, and denote by ± b ℑ( D ) the multiplicative group of all invertible fractional ideals of D , ordered by A ≤ B if and only if A ⊇ B . Denote by G i the value group of the valuation associated with the valuation ring D M i , where { M i } i ∈ I is the collection of all maximal ideals of D . In this note we prove that the natural map from ± b ℑ( D ) into ± b ∏ i ∈ I G i is an isomorphism onto the cardinal sum ± b ∐ i ∈ I G i if and only if D is h -local. As a corollary, the group of divisibility of an h -local Bézout domain is isomorphic to ± b ∐ i ∈ I G i , the notation being as above. [ABSTRACT FROM AUTHOR]

After the proof of a not very known refinement of the Noether Normalization Theorem, we obtain two sharp degree bounds for the geometric degree of a dominating morphism of irreducible affine algebraic varieties and for the degree of the components of the inverse of an isomorphism of such varieties, generalizing by this way the well-known Gabber bound for automorphisms of affine spaces. [ABSTRACT FROM AUTHOR]

In this paper we examine isomorphism classes of algebras which are generalizations of the enveloping algebra of the Heisenberg Lie algebra. [ABSTRACT FROM AUTHOR]

We determine the number of elements of order two in the group of normalized units V(F2G) of the group algebra F2G of a 2-group of maximal class over the field F2 of two elements. As a consequence for the 2-groups G and H of maximal class we have that V(F2G) and V(F2H) are isomorphic if and only if G and H are isomorphic. [ABSTRACT FROM AUTHOR]

Let (A, B, f) and (U, V, g) be C-algebras and ψ : (A, B, f) → (U, V, g) a C-algebra homomorphism. Let (A, Bˆf, f) and (U, Vˆg, g) be the dual C-algebras of (A, B, f) and (U, V, g), respectively. In this article we define a dual morphism ψˆ : (U, Vˆg, g) →  (A, Bˆf, f) for ψ, and use this dual morphism to establish the bijection between the quotient subsets of B and the C-subsets of its dual Bˆf obtained in [Blau, H. I. (1995a). Quotient Structures in C-algebras. J. Algebra 177:297–337]. This approach provides a conceptual proof of this very important bijection. [ABSTRACT FROM AUTHOR]

We prove that for a smooth projective variety X of dimension d defined over a finite field k, the structure map σ : X [xrarr] Spec k induces an isomorphism σ∗ : CHd+1(X, 1) ≅ CH1(k, 1) = k*. We also prove that the higher Chow groups CHd+s−1(X, s) of one-dimensional cycles are torsion for s ≥ 2. [ABSTRACT FROM AUTHOR]

In the case when R is a Dedekind domain of positive prime characteristic p > 0, we give a parameterisation of the isomorphism classes of the injective indecomposable R∞-modules. Here R∞ is the smallest ring extension of R on which the Frobenius morphism acts bijectively. Further, in this case, every injective R∞-module is the injective hull of a direct sum of injective indecomposable R∞-modules. [ABSTRACT FROM AUTHOR]

We describe the Lie isomorphisms on associative H*-algebras with zero annihilator. [ABSTRACT FROM AUTHOR]