Hochschild cohomology of Frobenius algebras
- Autores
- Guccione, Jorge Alberto; Guccione, Juan Jose
- Año de publicación
- 2003
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let k be a field, A a finite dimensional Frobenius k-algebra and φ: A→ A, the Nakayama automorphism of A with respect to a Frobenius homomorphism φ: A→ A,. Assume that φ has finite order m and that k has a primitive m-th root of unity w. Consider the decomposition A = A_0 ⊕...⊕ A_{m-1} of A, obtained defining A_i = {a ∈ A:φ(a) = w^i a}, and the decomposition HH^*(A) = ⊕_{i=0}^{m-1} HH_i^*(A) of the Hochschild cohomology of A, obtained from the decomposition of A. In this paper we prove that HH^*(A) = HH^*_0(A) and that if decomposition of A is strongly Z/m Z-graded, then Z/mZ acts on HH^*(A_0) and HH^*(A) = HH_0^*(A) = HH^*(A_0)^{Z/mZ}.
Fil: Guccione, Jorge Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
Fil: Guccione, Juan Jose. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
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- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/109657
Ver los metadatos del registro completo
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Hochschild cohomology of Frobenius algebrasGuccione, Jorge AlbertoGuccione, Juan Josehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let k be a field, A a finite dimensional Frobenius k-algebra and φ: A→ A, the Nakayama automorphism of A with respect to a Frobenius homomorphism φ: A→ A,. Assume that φ has finite order m and that k has a primitive m-th root of unity w. Consider the decomposition A = A_0 ⊕...⊕ A_{m-1} of A, obtained defining A_i = {a ∈ A:φ(a) = w^i a}, and the decomposition HH^*(A) = ⊕_{i=0}^{m-1} HH_i^*(A) of the Hochschild cohomology of A, obtained from the decomposition of A. In this paper we prove that HH^*(A) = HH^*_0(A) and that if decomposition of A is strongly Z/m Z-graded, then Z/mZ acts on HH^*(A_0) and HH^*(A) = HH_0^*(A) = HH^*(A_0)^{Z/mZ}.Fil: Guccione, Jorge Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Guccione, Juan Jose. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaAmerican Mathematical Society2003-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/109657Guccione, Jorge Alberto; Guccione, Juan Jose; Hochschild cohomology of Frobenius algebras; American Mathematical Society; Proceedings of the American Mathematical Society; 132; 5; 12-2003; 1241-12500002-99391088-6826CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-03-07350-7info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2004-132-05/S0002-9939-03-07350-7/S0002-9939-03-07350-7.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:46:02Zoai:ri.conicet.gov.ar:11336/109657instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:46:03.23CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
Hochschild cohomology of Frobenius algebras |
| title |
Hochschild cohomology of Frobenius algebras |
| spellingShingle |
Hochschild cohomology of Frobenius algebras Guccione, Jorge Alberto |
| 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, Jorge Alberto Guccione, Juan Jose |
| author |
Guccione, Jorge Alberto |
| author_facet |
Guccione, Jorge Alberto Guccione, Juan Jose |
| author_role |
author |
| author2 |
Guccione, Juan Jose |
| author2_role |
author |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
Let k be a field, A a finite dimensional Frobenius k-algebra and φ: A→ A, the Nakayama automorphism of A with respect to a Frobenius homomorphism φ: A→ A,. Assume that φ has finite order m and that k has a primitive m-th root of unity w. Consider the decomposition A = A_0 ⊕...⊕ A_{m-1} of A, obtained defining A_i = {a ∈ A:φ(a) = w^i a}, and the decomposition HH^*(A) = ⊕_{i=0}^{m-1} HH_i^*(A) of the Hochschild cohomology of A, obtained from the decomposition of A. In this paper we prove that HH^*(A) = HH^*_0(A) and that if decomposition of A is strongly Z/m Z-graded, then Z/mZ acts on HH^*(A_0) and HH^*(A) = HH_0^*(A) = HH^*(A_0)^{Z/mZ}. Fil: Guccione, Jorge Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina Fil: Guccione, Juan Jose. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina |
| description |
Let k be a field, A a finite dimensional Frobenius k-algebra and φ: A→ A, the Nakayama automorphism of A with respect to a Frobenius homomorphism φ: A→ A,. Assume that φ has finite order m and that k has a primitive m-th root of unity w. Consider the decomposition A = A_0 ⊕...⊕ A_{m-1} of A, obtained defining A_i = {a ∈ A:φ(a) = w^i a}, and the decomposition HH^*(A) = ⊕_{i=0}^{m-1} HH_i^*(A) of the Hochschild cohomology of A, obtained from the decomposition of A. In this paper we prove that HH^*(A) = HH^*_0(A) and that if decomposition of A is strongly Z/m Z-graded, then Z/mZ acts on HH^*(A_0) and HH^*(A) = HH_0^*(A) = HH^*(A_0)^{Z/mZ}. |
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2003 |
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2003-12 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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http://hdl.handle.net/11336/109657 Guccione, Jorge Alberto; Guccione, Juan Jose; Hochschild cohomology of Frobenius algebras; American Mathematical Society; Proceedings of the American Mathematical Society; 132; 5; 12-2003; 1241-1250 0002-9939 1088-6826 CONICET Digital CONICET |
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http://hdl.handle.net/11336/109657 |
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Guccione, Jorge Alberto; Guccione, Juan Jose; Hochschild cohomology of Frobenius algebras; American Mathematical Society; Proceedings of the American Mathematical Society; 132; 5; 12-2003; 1241-1250 0002-9939 1088-6826 CONICET Digital CONICET |
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eng |
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eng |
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