The Hochschild cohomology algebra for a family of self-injective algebras of the tree class $D_{n}$

DOI10.1090/S1061-0022-2012-01220-3zbMath1280.16012OpenAlexW2008029494WikidataQ58174630 ScholiaQ58174630MaRDI QIDQ2849073

Yu. V. Volkov

Publication date: 16 September 2013

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-2012-01220-3

zbMATH Keywords

Hochschild cohomology groupsprojective bimodule resolutionsrepresentation-finite self-injective algebras

Mathematics Subject Classification ID

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

Related Items

BV differential on Hochschild cohomology of Frobenius algebras ⋮ Hochschild cohomology for algebras of semidihedral type. VI: The family \(SD(2\mathcal{B})_2\) in characteristic different from 2 ⋮ Hochschild cohomology for algebras of semidihedral type. VII: Algebras with a small parameter ⋮ Hochschild cohomology of algebras of quaternion type. IV: Cohomology algebra for exceptional local algebras ⋮ Hochschild cohomology for self-injective algebras of tree class \(D_n\). VI. ⋮ Hochschild cohomology for algebras of dihedral type. IV: The family \(D(2\mathcal B)(k,s,0)\). ⋮ Hochschild cohomology for algebras of dihedral type. V. the family \(D(3\mathcal{K})\) in characteristic different from 2 ⋮ Hochschild cohomology of algebras of semidihedral type. V: The family \( SD\left(3\mathcal{K}\right) \) ⋮ Hochschild cohomology of algebras of semidihedral type. IV: The cohomology algebra for the family \(SD(2\mathcal B)_2(k,t,c)\) in the case \(c=0\). ⋮ Hochschild cohomology of algebras of dihedral type. VIII: Hochshild cohomology algebra for the family \(D(2\mathcal{B})(k, s, 0)\) in characteristic 2 ⋮ Hochschild comohology for algebras of dihedral type, VI. The family $D(2\mathcal B)(k,s,1)$

Cites Work

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• Periodic resolutions and self-injective algebras of finite type.
• Stable equivalence classes of self-injective algebras of tree class \(D_n\).
• Algebren, Darstellungsköcher, Überlagerungen und zurück
• Twisted bimodules and Hochschild cohomology for self-injective algebras of class \(A_n\). II.
• Bimodule resolutions of Möbius algebras
• Twisted bimodules and Hochschild cohomology for self-injective algebras of class An