Hochschild cohomology algebra of abelian groups

DOI10.1007/PL00000389zbMath0872.16004OpenAlexW2033963432MaRDI QIDQ1359057

Claude Cibils, Andrea L. Solotar

Publication date: 19 August 1997

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/pl00000389

zbMATH Keywords

finite Abelian groupsHochschild cohomology algebrasmonoidal categories of Hopf bimodules

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Group rings (16S34) (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) (13D03) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

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Cites Work

• Unnamed Item
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• Quantum path algebras
• Cyclic homology of algebras with one generator
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Algèbres enveloppantes quantifiées, groupes quantiques compacts de matrices et calcul différentiel non commutatif. (Quantized enveloping algebras, compact quantum matrix groups and noncommutative differential calculus)
• Tensor product of Hopf bimodules over a group
• The hochschild cohomology ring of a modular group algebra: the commutative case