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
- 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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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/ar2025-09-29T13:42:51Zpaperaa: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:18962025-09-29 13:42:53.122Biblioteca 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 http://purl.org/coar/resource_type/c_6501 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 http://creativecommons.org/licenses/by/2.5/ar |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
http://creativecommons.org/licenses/by/2.5/ar |
dc.format.none.fl_str_mv |
application/pdf |
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 |
reponame_str |
Biblioteca Digital (UBA-FCEN) |
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Biblioteca Digital (UBA-FCEN) |
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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 |
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ana@bl.fcen.uba.ar |
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