A. I. Generalov

Cohomology of Algebras of Dihedral Type. I

A technique which is associated with the Benson―Carlson diagrammatic method is developed. Using this technique, we describe the Yoneda algebras of the algebras that constitute a series of algebras of dihedral type. We also describe the Ext-algebras of simple modules over the algebras considered. Bibliography: 6 titles.

Basic Submodules of Modules Over Serial, Right Noetherian Rings. II

In the preceding paper, the authors published an existence theorem for basic submodules of right modules over right Noetherian, serial rings. The aim of the present paper is to prove a uniqueness theorem for basic submodules over such rings. Bibliography: 13 titles.

Hochschild cohomology of algebras of dihedral type. II. Local algebras

For local algebras that constitute a family of algebras of dihedral type, the Hochschild cohomology is calculated in the case where the base algebraically closed field has a characteristic different from 2. Furthermore, a description of the Hochschild cohomology algebra (in terms of generators and relations) is given for the local algebras under consideration. In relevant calculations, a beforehand constructed bimodule resolution for these algebras is used. Bibliography: 19 titles.

The Yoneda Algebras of Möbius Algebras

The Yoneda algebras of Möbius algebras are described in terms of quivers with relations. Bibliography: 10 titles.

The Yoneda Algebras of Serial QF-Algebras

The Yoneda algebras of serial QF-algebras over an algebraically closed field k are described in terms of quivers with relations. We also describe the Ext-algebras of simple modules over the k-algebras in question. Bibliography: 7 titles.

Decomposition of the Grothendieck group of stable categories of finite groups.

AbstractLet G be a finite group with a normal Sylow p-subgroup H such that the corresponding quotient is Abelian. We prove that the Grothendieck group of the stable category of G (over an algebraically closed field of characteristic p) contains a cyclic direct summand of order

On the construction of bimodule resolutions with the help of the Happel lemma

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Cohomology of Algebras of Semidihedral Type. III: The Family SD(3\(\mathcal{K}\))

. Bibliography: 6 titles.