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Journal of Mathematical Sciences

, Volume 161, Issue 4, pp 530–536 | Cite as

Cohomology of algebras of semidihedral type. VII. Local algebras

  • A. I. Generalov
Article
  • 21 Downloads

The present paper continues a cycle of papers, in which the Yoneda algebras were calculated for several families of algebras of dihedral and semidihedral type in the classification by K. Erdmann. Using the technique of a previous paper, a description of the Yoneda algebras for both families of local algebras occurring in this classification is given. Namely, a conjecture about the structure of the minimal free resolution of a (unique) simple module is stated, which is based on some empirical observations, and after establishing this conjecture, “cohomology information" is derived from the resolution discovered, and, as a result, this allows us to describe the Yoneda algebras of the algebras under consideration, It is noted that a similar technique was applied in computation of the Hochschild cohomology algebra for some finite-dimensional algebras. Bibliography: 23 titles.

Keywords

Russia Similar Technique Empirical Observation Simple Module Free Resolution 
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© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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