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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todo:paper_0003889X_v68_n1_p17_Cibils2023-10-03T13:56:42Z Hochschild cohomology algebra of abelian groups Cibils, C. Solotar, A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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. |
| format |
JOUR |
| author |
Cibils, C. Solotar, A. |
| spellingShingle |
Cibils, C. Solotar, A. Hochschild cohomology algebra of abelian groups |
| author_facet |
Cibils, C. Solotar, A. |
| author_sort |
Cibils, C. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_0003889X_v68_n1_p17_Cibils |
| work_keys_str_mv |
AT cibilsc hochschildcohomologyalgebraofabeliangroups AT solotara hochschildcohomologyalgebraofabeliangroups |
| _version_ |
1782027989803859968 |