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In this paper, the authors consider the range of a certain class of ASH algebras in [An, Q., Elliott, G. A., Li, Z. and Liu, Z., The classification of certain ASH C*-algebras of real rank zero, J. Topol. Anal., 14(1), 2022, 183–202], which is under the scheme of the Elliott program in the setting of real rank zero C*-algebras. As a reduction theorem, they prove that all these ASH algebras are still the AD algebras studied in [Dadarlat, M. and Loring, T. A., Classifying C*-algebras via ordered, mod-p K-theory, Math. Ann., 305, 1996, 601–616]. [ABSTRACT FROM AUTHOR]

Recently, some concepts such as Hom-algebras, Hom-Lie algebras, Hom-Lie admissible algebras, Hom-coalgebras are studied and some classical properties of algebras and some geometric objects are extended on them. In this paper by recalling the concept of Hom-ρ-commutative algebras, the authurs intend to develop some of the most classical results in Riemannian geometry such as metric, connection, torsion tensor, curvature tensor on it and also they discuss about differential operators and get some results of differential calculus by using them. The notions of symplectic structures and Poisson structures are included and an example of ρ-Poisson bracket is given. [ABSTRACT FROM AUTHOR]

This paper gives the concept of the reduced pro-Banach algebra crossed product associated with inversely pro-Banach algebra dynamical system, and shows that the reduced crossed product is an inverse limit of an inverse system of Banach algebra crossed products. Also, the authors show that if the locally compact group is amenable, then the crossed product and the reduced crossed product are isometrically isomorphic. [ABSTRACT FROM AUTHOR]

In this paper, the authors give a new proof of Block and Weinberger's Bochner vanishing theorem built on direct computations in the K-theory of the localization algebra. [ABSTRACT FROM AUTHOR]

Elliott dimension drop interval algebra is an important class among all C*-algebras in the classification theory. Especially, they are building stones of A H D algebra and the latter contains all AH algebras with the ideal property of no dimension growth. In this paper, the authors will show two decomposition theorems related to the Elliott dimension drop interval algebra. Their results are key steps in classifying all AH algebras with the ideal property of no dimension growth. [ABSTRACT FROM AUTHOR]

Let F be an algebraically closed field of prime characteristic, and W(m, n, 1) be the simple restricted Lie superalgebra of Witt type over F, which is the Lie superalgebra of superderivations of the superalgebra A (m ; 1) ⊗ ∧ (n) , where A (m ; 1) is the truncated polynomial algebra with m indeterminants and ∧(n) is the Grassmann algebra with n indeterminants. In this paper, the author determines the character formulas for a class of simple restricted modules of W(m, n, 1) with atypical weights of type I. [ABSTRACT FROM AUTHOR]

Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the persistence approximation property for maximal Roe algebras. They show that persistence approximation property of maximal Roe algebras follows from maximal coarse Baum-Connes conjecture. In particular, let X be a discrete metric space with bounded geometry, assume that X admits a fibred coarse embedding into Hilbert space and X is coarsely uniformly contractible, then C*max(X) has persistence approximation property. The authors also give an application of the quantitative K-theory to the maximal coarse Baum-Connes conjecture. [ABSTRACT FROM AUTHOR]

Given a triangle functor F: A→B, the authors introduce the half image hImF, which is an additive category closely related to F. If F is full or faithful, then hImF admits a natural triangulated structure. However, in general, one can not expect that hImF has a natural triangulated structure. The aim of this paper is to prove that hImF admits a natural triangulated structure if and only if F satisfies the condition (SM). If this is the case, hImF is triangle-equivalent to the Verdier quotient A/KerF. [ABSTRACT FROM AUTHOR]

Let D be an integer at least 3 and let H( D, 2) denote the hypercube. It is known that H( D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all { D − 2 i}, Suppose that ⊠ denotes the tetrahedron algebra. In this paper, the authors display an action of ⊠ on the standard module V of H( D, 2). To describe this action, the authors define six matrices in Mat(ℂ), called Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ⊠ on V. [ABSTRACT FROM AUTHOR]

The purpose is to introduce the notions of 3-Bihom-ρ-Lie algebras and 3-pre-Bihom-ρ-Lie algebras. The authors describe their constructions and express the related lemmas and theorems. Also, they define the 3-Bihom-ρ-Leibniz algebras and show that a 3-Bihom-ρ-Lie algebra is a 3-Bihom-ρ-Leibniz algebra with the ρ-Bihom-skew symmetry property. Moreover, a combination of a 3-Bihom-ρ-Lie algebra bracket and a Rota-Baxer operator gives a 3-pre-Bihom-ρ-Lie algebra structure. [ABSTRACT FROM AUTHOR]

The weak finite determinacy of relative map-germs is studied. The authors first give the concept of weak finite determination, and then give several sufficient conditions for a relative map-germ to be weak finitely determined, which is an important complement to Mather's work. Moreover, as an application, it is proven that the relative stable map-germs are weak finitely determined. [ABSTRACT FROM AUTHOR]