The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines

Autores
Kordon, Francisco; Suárez-Alvarez, Mariano
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given a central arrangement of lines A in a 2-dimensional vector space V over a field of characteristic zero, we study the algebra D (A) of differential operators on V which are logarithmic along A. Among other things we determine the Hochschild cohomology of D (A) as a Gerstenhaber algebra, establish a connection between that cohomology and the de Rham cohomology of the complement M(A) of the arrangement, determine the isomorphism group of D (A) and classify the algebras of that form up to isomorphism.
Fil: Kordon, Francisco. 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
Fil: Suárez-Alvarez, Mariano. 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
ARRANGEMENT OF HYPERPLANES
DIFFERENTIAL OPERATORS
HOCHSCHILD COHOMOLOGY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/215003
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of linesKordon, FranciscoSuárez-Alvarez, MarianoARRANGEMENT OF HYPERPLANESDIFFERENTIAL OPERATORSHOCHSCHILD COHOMOLOGYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a central arrangement of lines A in a 2-dimensional vector space V over a field of characteristic zero, we study the algebra D (A) of differential operators on V which are logarithmic along A. Among other things we determine the Hochschild cohomology of D (A) as a Gerstenhaber algebra, establish a connection between that cohomology and the de Rham cohomology of the complement M(A) of the arrangement, determine the isomorphism group of D (A) and classify the algebras of that form up to isomorphism.Fil: Kordon, Francisco. 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"; ArgentinaFil: Suárez-Alvarez, Mariano. 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"; ArgentinaUniversität Bielefeld2022-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/215003Kordon, Francisco; Suárez-Alvarez, Mariano; The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines; Universität Bielefeld; Documenta Mathematica; 27; 6-2022; 869-9161431-0643CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://ems.press/journals/dm/articles/8965818info:eu-repo/semantics/altIdentifier/doi/10.25537/dm.2022v27.869-916info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:56:08Zoai:ri.conicet.gov.ar:11336/215003instacron: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:34982025-10-22 11:56:08.336CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines
title The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines
spellingShingle The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines
Kordon, Francisco
ARRANGEMENT OF HYPERPLANES
DIFFERENTIAL OPERATORS
HOCHSCHILD COHOMOLOGY
title_short The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines
title_full The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines
title_fullStr The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines
title_full_unstemmed The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines
title_sort The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines
dc.creator.none.fl_str_mv Kordon, Francisco
Suárez-Alvarez, Mariano
author Kordon, Francisco
author_facet Kordon, Francisco
Suárez-Alvarez, Mariano
author_role author
author2 Suárez-Alvarez, Mariano
author2_role author
dc.subject.none.fl_str_mv ARRANGEMENT OF HYPERPLANES
DIFFERENTIAL OPERATORS
HOCHSCHILD COHOMOLOGY
topic ARRANGEMENT OF HYPERPLANES
DIFFERENTIAL OPERATORS
HOCHSCHILD COHOMOLOGY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given a central arrangement of lines A in a 2-dimensional vector space V over a field of characteristic zero, we study the algebra D (A) of differential operators on V which are logarithmic along A. Among other things we determine the Hochschild cohomology of D (A) as a Gerstenhaber algebra, establish a connection between that cohomology and the de Rham cohomology of the complement M(A) of the arrangement, determine the isomorphism group of D (A) and classify the algebras of that form up to isomorphism.
Fil: Kordon, Francisco. 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
Fil: Suárez-Alvarez, Mariano. 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 Given a central arrangement of lines A in a 2-dimensional vector space V over a field of characteristic zero, we study the algebra D (A) of differential operators on V which are logarithmic along A. Among other things we determine the Hochschild cohomology of D (A) as a Gerstenhaber algebra, establish a connection between that cohomology and the de Rham cohomology of the complement M(A) of the arrangement, determine the isomorphism group of D (A) and classify the algebras of that form up to isomorphism.
publishDate 2022
dc.date.none.fl_str_mv 2022-06
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/11336/215003
Kordon, Francisco; Suárez-Alvarez, Mariano; The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines; Universität Bielefeld; Documenta Mathematica; 27; 6-2022; 869-916
1431-0643
CONICET Digital
CONICET
url http://hdl.handle.net/11336/215003
identifier_str_mv Kordon, Francisco; Suárez-Alvarez, Mariano; The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines; Universität Bielefeld; Documenta Mathematica; 27; 6-2022; 869-916
1431-0643
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ems.press/journals/dm/articles/8965818
info:eu-repo/semantics/altIdentifier/doi/10.25537/dm.2022v27.869-916
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Universität Bielefeld
publisher.none.fl_str_mv Universität Bielefeld
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 12.982451

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