The structure of smooth algebras in Kapranov's framework for noncommutative geometry

Autores
Cortiñas, Guillermo Horacio
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In Kapranov, M. Noncommutative geometry based on commutator expansions, J. reine angew. Math 505 (1998) 73-118, a theory of noncommutative algebraic varieties was proposed. Here we prove a structure theorem for the noncommutative coordinate rings of affine open subsets of such of those varieties which are smooth (Theorem 3.4). The theorem describes the local ring of a point as a truncation of a quantization of the enveloping Poisson algebra of a smooth commutative local algebra. An explicit descripition of this quantization is given in Theorem 2.5. A description of the A- module structure of the Poisson envelope of a smooth commutative algebra A was given in loc. cit., Theorem 4.1.3. However the proof given in loc. cit. has a gap. We fix this gap for A local (Theorem 1.4) and prove a weaker global result (Theorem 1.6).
Fil: Cortiñas, Guillermo Horacio. 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
Materia
COMMUTATOR FILTRATION
POISSON ALGEBRA
D-SMOOTH ALGEBRA
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
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oai:ri.conicet.gov.ar:11336/155134
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spelling The structure of smooth algebras in Kapranov's framework for noncommutative geometryCortiñas, Guillermo HoracioCOMMUTATOR FILTRATIONPOISSON ALGEBRAD-SMOOTH ALGEBRAhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In Kapranov, M. Noncommutative geometry based on commutator expansions, J. reine angew. Math 505 (1998) 73-118, a theory of noncommutative algebraic varieties was proposed. Here we prove a structure theorem for the noncommutative coordinate rings of affine open subsets of such of those varieties which are smooth (Theorem 3.4). The theorem describes the local ring of a point as a truncation of a quantization of the enveloping Poisson algebra of a smooth commutative local algebra. An explicit descripition of this quantization is given in Theorem 2.5. A description of the A- module structure of the Poisson envelope of a smooth commutative algebra A was given in loc. cit., Theorem 4.1.3. However the proof given in loc. cit. has a gap. We fix this gap for A local (Theorem 1.4) and prove a weaker global result (Theorem 1.6).Fil: Cortiñas, Guillermo Horacio. 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"; ArgentinaAcademic Press Inc Elsevier Science2004-11info: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/11336/155134Cortiñas, Guillermo Horacio; The structure of smooth algebras in Kapranov's framework for noncommutative geometry; Academic Press Inc Elsevier Science; Journal of Algebra; 281; 2; 11-2004; 679-6940021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2004.08.002info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869304004272?via%3Dihubinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/math/0002177info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-08-25T14:50:35Zoai:ri.conicet.gov.ar:11336/155134instacron: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:34982026-08-25 14:50:35.37CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The structure of smooth algebras in Kapranov's framework for noncommutative geometry
title The structure of smooth algebras in Kapranov's framework for noncommutative geometry
spellingShingle The structure of smooth algebras in Kapranov's framework for noncommutative geometry
Cortiñas, Guillermo Horacio
COMMUTATOR FILTRATION
POISSON ALGEBRA
D-SMOOTH ALGEBRA
title_short The structure of smooth algebras in Kapranov's framework for noncommutative geometry
title_full The structure of smooth algebras in Kapranov's framework for noncommutative geometry
title_fullStr The structure of smooth algebras in Kapranov's framework for noncommutative geometry
title_full_unstemmed The structure of smooth algebras in Kapranov's framework for noncommutative geometry
title_sort The structure of smooth algebras in Kapranov's framework for noncommutative geometry
dc.creator.none.fl_str_mv Cortiñas, Guillermo Horacio
author Cortiñas, Guillermo Horacio
author_facet Cortiñas, Guillermo Horacio
author_role author
dc.subject.none.fl_str_mv COMMUTATOR FILTRATION
POISSON ALGEBRA
D-SMOOTH ALGEBRA
topic COMMUTATOR FILTRATION
POISSON ALGEBRA
D-SMOOTH ALGEBRA
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In Kapranov, M. Noncommutative geometry based on commutator expansions, J. reine angew. Math 505 (1998) 73-118, a theory of noncommutative algebraic varieties was proposed. Here we prove a structure theorem for the noncommutative coordinate rings of affine open subsets of such of those varieties which are smooth (Theorem 3.4). The theorem describes the local ring of a point as a truncation of a quantization of the enveloping Poisson algebra of a smooth commutative local algebra. An explicit descripition of this quantization is given in Theorem 2.5. A description of the A- module structure of the Poisson envelope of a smooth commutative algebra A was given in loc. cit., Theorem 4.1.3. However the proof given in loc. cit. has a gap. We fix this gap for A local (Theorem 1.4) and prove a weaker global result (Theorem 1.6).
Fil: Cortiñas, Guillermo Horacio. 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
description In Kapranov, M. Noncommutative geometry based on commutator expansions, J. reine angew. Math 505 (1998) 73-118, a theory of noncommutative algebraic varieties was proposed. Here we prove a structure theorem for the noncommutative coordinate rings of affine open subsets of such of those varieties which are smooth (Theorem 3.4). The theorem describes the local ring of a point as a truncation of a quantization of the enveloping Poisson algebra of a smooth commutative local algebra. An explicit descripition of this quantization is given in Theorem 2.5. A description of the A- module structure of the Poisson envelope of a smooth commutative algebra A was given in loc. cit., Theorem 4.1.3. However the proof given in loc. cit. has a gap. We fix this gap for A local (Theorem 1.4) and prove a weaker global result (Theorem 1.6).
publishDate 2004
dc.date.none.fl_str_mv 2004-11
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/11336/155134
Cortiñas, Guillermo Horacio; The structure of smooth algebras in Kapranov's framework for noncommutative geometry; Academic Press Inc Elsevier Science; Journal of Algebra; 281; 2; 11-2004; 679-694
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/155134
identifier_str_mv Cortiñas, Guillermo Horacio; The structure of smooth algebras in Kapranov's framework for noncommutative geometry; Academic Press Inc Elsevier Science; Journal of Algebra; 281; 2; 11-2004; 679-694
0021-8693
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2004.08.002
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869304004272?via%3Dihub
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/math/0002177
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.265058

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