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Cohomology of algebras of semidihedral type. VII. Local algebras

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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.

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  1. St. Petersburg State University, St. Petersburg, Russia

    A. I. Generalov

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  1. A. I. Generalov
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Correspondence to A. I. Generalov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 365, 2009, pp. 130–142.

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Generalov, A.I. Cohomology of algebras of semidihedral type. VII. Local algebras. J Math Sci 161, 530–536 (2009). https://doi.org/10.1007/s10958-009-9581-1

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