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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Autores principales: Guccione, Jorge Alberto, Guccione, Juan José
Publicado: 2004
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v132_n5_p1241_Guccione
http://hdl.handle.net/20.500.12110/paper_00029939_v132_n5_p1241_Guccione
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00029939_v132_n5_p1241_Guccione
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spelling paper:paper_00029939_v132_n5_p1241_Guccione2023-06-08T14:23:26Z Hochschild cohomology of Frobenius algebras Guccione, Jorge Alberto Guccione, Juan José 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. 2004 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v132_n5_p1241_Guccione http://hdl.handle.net/20.500.12110/paper_00029939_v132_n5_p1241_Guccione
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection 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.
author Guccione, Jorge Alberto
Guccione, Juan José
spellingShingle Guccione, Jorge Alberto
Guccione, Juan José
Hochschild cohomology of Frobenius algebras
author_facet Guccione, Jorge Alberto
Guccione, Juan José
author_sort Guccione, Jorge Alberto
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
publishDate 2004
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v132_n5_p1241_Guccione
http://hdl.handle.net/20.500.12110/paper_00029939_v132_n5_p1241_Guccione
work_keys_str_mv AT guccionejorgealberto hochschildcohomologyoffrobeniusalgebras
AT guccionejuanjose hochschildcohomologyoffrobeniusalgebras
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