Hochschild cohomology of Frobenius algebras
Let k be a field, A a finite-dimensional Frobenius k-algebra and ρ: A → A, the Nakayama automorphism of A with respect to a Frobenius homomorphism φ: A → k. Assume that k has finite order m and that k has a primitive m-th root of unity w. Consider the decomposition A = A0 ⊕ ... ⊕ Am-1 of A, obtained...
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todo:paper_00029939_v132_n5_p1241_Guccione2023-10-03T13:55:07Z Hochschild cohomology of Frobenius algebras Guccione, J.A. Guccione, J.J. Let k be a field, A a finite-dimensional Frobenius k-algebra and ρ: A → A, the Nakayama automorphism of A with respect to a Frobenius homomorphism φ: A → k. Assume that k has finite order m and that k has a primitive m-th root of unity w. Consider the decomposition A = A0 ⊕ ... ⊕ Am-1 of A, obtained by defining Ai = {a ∈ A : ρ(a) = wia}, and the decomposition HH*(A) = ⊕i=0 m-1 HHi* Hochschild cohomology of A, obtained from the decomposition of A. In this paper we prove that HH*(A) = HH0*(A) and that if the decomposition of A is strongly ℤ/mℤ-graded, then ℤ/mℤ acts on HH*(A 0) and HH*(A) = HH0*(A) = HH*(A 0)ℤ/mℤ. Fil:Guccione, J.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Guccione, J.J. 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_00029939_v132_n5_p1241_Guccione |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
Let k be a field, A a finite-dimensional Frobenius k-algebra and ρ: A → A, the Nakayama automorphism of A with respect to a Frobenius homomorphism φ: A → k. Assume that k has finite order m and that k has a primitive m-th root of unity w. Consider the decomposition A = A0 ⊕ ... ⊕ Am-1 of A, obtained by defining Ai = {a ∈ A : ρ(a) = wia}, and the decomposition HH*(A) = ⊕i=0 m-1 HHi* Hochschild cohomology of A, obtained from the decomposition of A. In this paper we prove that HH*(A) = HH0*(A) and that if the decomposition of A is strongly ℤ/mℤ-graded, then ℤ/mℤ acts on HH*(A 0) and HH*(A) = HH0*(A) = HH*(A 0)ℤ/mℤ. |
| format |
JOUR |
| author |
Guccione, J.A. Guccione, J.J. |
| spellingShingle |
Guccione, J.A. Guccione, J.J. Hochschild cohomology of Frobenius algebras |
| author_facet |
Guccione, J.A. Guccione, J.J. |
| author_sort |
Guccione, J.A. |
| title |
Hochschild cohomology of Frobenius algebras |
| title_short |
Hochschild cohomology of Frobenius algebras |
| title_full |
Hochschild cohomology of Frobenius algebras |
| title_fullStr |
Hochschild cohomology of Frobenius algebras |
| title_full_unstemmed |
Hochschild cohomology of Frobenius algebras |
| title_sort |
hochschild cohomology of frobenius algebras |
| url |
http://hdl.handle.net/20.500.12110/paper_00029939_v132_n5_p1241_Guccione |
| work_keys_str_mv |
AT guccioneja hochschildcohomologyoffrobeniusalgebras AT guccionejj hochschildcohomologyoffrobeniusalgebras |
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1807314699803426816 |