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Hochschild cohomology for self-injective algebras of tree class \(D_n\). II. (English. Russian original) Zbl 1197.16009

J. Math. Sci., New York 161, No. 4, 492-524 (2009); translation from Zap. Nauchn. Semin. POMI 365, 63-121 (2009).
Summary: The minimal projective bimodule resolution for a certain family of representation-finite self-injective algebras of tree class \(D_n\) is constructed. The dimensions of the groups of Hochschild cohomology for the algebras under consideration are calculated by the instrumentality of this resolution. The resolution constructed is periodic, and accordingly the Hochschild cohomology for these algebras is periodic as well.

MSC:

16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
16G20 Representations of quivers and partially ordered sets
16G60 Representation type (finite, tame, wild, etc.) of associative algebras
16E05 Syzygies, resolutions, complexes in associative algebras
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References:

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