Hochschild cohomology algebra of abelian groups

In this paper we present a direct proof of what is suggested by Holm's results (T. Holm, The Hochschild cohomology ring of a modular group algebra: the commutative case, Comm. Algebra 24, 1957-1969 (1996)): there is an isomorphism of algebras HH*(kG, kG) → kG ⊗ H*(G, k) where G is a finite abel...

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Autor principal: Solotar, Andrea Leonor
Publicado: 1997
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0003889X_v68_n1_p17_Cibils
http://hdl.handle.net/20.500.12110/paper_0003889X_v68_n1_p17_Cibils
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_0003889X_v68_n1_p17_Cibils2023-06-08T14:24:47Z Hochschild cohomology algebra of abelian groups Solotar, Andrea Leonor In this paper we present a direct proof of what is suggested by Holm's results (T. Holm, The Hochschild cohomology ring of a modular group algebra: the commutative case, Comm. Algebra 24, 1957-1969 (1996)): there is an isomorphism of algebras HH*(kG, kG) → kG ⊗ H*(G, k) where G is a finite abelian group, k a ring, HH*(kG, kG) is the Hochschild cohomology algebra and H*(G, k) the usual cohomology algebra. This result agrees with the well-known additive structure result in force for any group G; we remark that the multiplicative structure result we have obtained is quite similar to the description of the monoidal category of Hopf bimodules over kG given in "C. Cibils, Tensor product of Hopf bimodules, to appear in Proc. Amer. Math. Soc.". This similarity leads to conjecture the structure of HH*(kG, kG) for G a finite group. Fil:Solotar, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1997 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0003889X_v68_n1_p17_Cibils http://hdl.handle.net/20.500.12110/paper_0003889X_v68_n1_p17_Cibils
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description In this paper we present a direct proof of what is suggested by Holm's results (T. Holm, The Hochschild cohomology ring of a modular group algebra: the commutative case, Comm. Algebra 24, 1957-1969 (1996)): there is an isomorphism of algebras HH*(kG, kG) → kG ⊗ H*(G, k) where G is a finite abelian group, k a ring, HH*(kG, kG) is the Hochschild cohomology algebra and H*(G, k) the usual cohomology algebra. This result agrees with the well-known additive structure result in force for any group G; we remark that the multiplicative structure result we have obtained is quite similar to the description of the monoidal category of Hopf bimodules over kG given in "C. Cibils, Tensor product of Hopf bimodules, to appear in Proc. Amer. Math. Soc.". This similarity leads to conjecture the structure of HH*(kG, kG) for G a finite group.
author Solotar, Andrea Leonor
spellingShingle Solotar, Andrea Leonor
Hochschild cohomology algebra of abelian groups
author_facet Solotar, Andrea Leonor
author_sort Solotar, Andrea Leonor
title Hochschild cohomology algebra of abelian groups
title_short Hochschild cohomology algebra of abelian groups
title_full Hochschild cohomology algebra of abelian groups
title_fullStr Hochschild cohomology algebra of abelian groups
title_full_unstemmed Hochschild cohomology algebra of abelian groups
title_sort hochschild cohomology algebra of abelian groups
publishDate 1997
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0003889X_v68_n1_p17_Cibils
http://hdl.handle.net/20.500.12110/paper_0003889X_v68_n1_p17_Cibils
work_keys_str_mv AT solotarandrealeonor hochschildcohomologyalgebraofabeliangroups
_version_ 1768543111114391552

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