Hochschild cohomology of Frobenius algebras

Autores
Guccione, J.A.; Guccione, J.J.
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fuente
Proc. Am. Math. Soc. 2004;132(5):1241-1250
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_00029939_v132_n5_p1241_Guccione
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spelling Hochschild cohomology of Frobenius algebrasGuccione, 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.2004info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00029939_v132_n5_p1241_GuccioneProc. Am. Math. Soc. 2004;132(5):1241-1250reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-10-23T11:18:14Zpaperaa:paper_00029939_v132_n5_p1241_GuccioneInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-10-23 11:18:16.294Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Hochschild cohomology of Frobenius algebras
title Hochschild cohomology of Frobenius algebras
spellingShingle Hochschild cohomology of Frobenius algebras
Guccione, J.A.
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
dc.creator.none.fl_str_mv Guccione, J.A.
Guccione, J.J.
author Guccione, J.A.
author_facet Guccione, J.A.
Guccione, J.J.
author_role author
author2 Guccione, J.J.
author2_role author
dc.description.none.fl_txt_mv 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.
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.
publishDate 2004
dc.date.none.fl_str_mv 2004
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.12110/paper_00029939_v132_n5_p1241_Guccione
url http://hdl.handle.net/20.500.12110/paper_00029939_v132_n5_p1241_Guccione
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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eu_rights_str_mv openAccess
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dc.source.none.fl_str_mv Proc. Am. Math. Soc. 2004;132(5):1241-1250
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
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instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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