Path on graphs and associated quantum groupoids

Autores
Trinchero, Roberto Carlos
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given any simple biorientable graph it is shown that there exists a weak *-Hopf algebra constructed on the vector space of graded endomorphisms of essential paths on the graph. This construction is based on a direct sum decomposition of the space of paths into orthogonal subspaces one of which is the space of essential paths. Two simple examples are worked out with certain detail, the ADE graph A3 and the affine graph A[2]. For the first example the weak *-Hopf algebra coincides with the so called double triangle algebra. No use is made of Ocneanu’s cell calculus.
Fil: Trinchero, Roberto Carlos. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Quantum groupoids
Conformal Field theory
Graphs
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
OAI Identificador
oai:ri.conicet.gov.ar:11336/9482
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Path on graphs and associated quantum groupoidsTrinchero, Roberto CarlosQuantum groupoidsConformal Field theoryGraphshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given any simple biorientable graph it is shown that there exists a weak *-Hopf algebra constructed on the vector space of graded endomorphisms of essential paths on the graph. This construction is based on a direct sum decomposition of the space of paths into orthogonal subspaces one of which is the space of essential paths. Two simple examples are worked out with certain detail, the ADE graph A3 and the affine graph A[2]. For the first example the weak *-Hopf algebra coincides with the so called double triangle algebra. No use is made of Ocneanu’s cell calculus.Fil: Trinchero, Roberto Carlos. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaUnión Matemática Argentina2010-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/9482Trinchero, Roberto Carlos; Path on graphs and associated quantum groupoids; Unión Matemática Argentina; Revista de la Unión Matemática Argentina ; 51; 2; 9-2010; 147-1700041-69321669-9637enginfo:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol51info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:00:05Zoai:ri.conicet.gov.ar:11336/9482instacron: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:34982025-10-15 15:00:05.739CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Path on graphs and associated quantum groupoids
title Path on graphs and associated quantum groupoids
spellingShingle Path on graphs and associated quantum groupoids
Trinchero, Roberto Carlos
Quantum groupoids
Conformal Field theory
Graphs
title_short Path on graphs and associated quantum groupoids
title_full Path on graphs and associated quantum groupoids
title_fullStr Path on graphs and associated quantum groupoids
title_full_unstemmed Path on graphs and associated quantum groupoids
title_sort Path on graphs and associated quantum groupoids
dc.creator.none.fl_str_mv Trinchero, Roberto Carlos
author Trinchero, Roberto Carlos
author_facet Trinchero, Roberto Carlos
author_role author
dc.subject.none.fl_str_mv Quantum groupoids
Conformal Field theory
Graphs
topic Quantum groupoids
Conformal Field theory
Graphs
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 any simple biorientable graph it is shown that there exists a weak *-Hopf algebra constructed on the vector space of graded endomorphisms of essential paths on the graph. This construction is based on a direct sum decomposition of the space of paths into orthogonal subspaces one of which is the space of essential paths. Two simple examples are worked out with certain detail, the ADE graph A3 and the affine graph A[2]. For the first example the weak *-Hopf algebra coincides with the so called double triangle algebra. No use is made of Ocneanu’s cell calculus.
Fil: Trinchero, Roberto Carlos. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Given any simple biorientable graph it is shown that there exists a weak *-Hopf algebra constructed on the vector space of graded endomorphisms of essential paths on the graph. This construction is based on a direct sum decomposition of the space of paths into orthogonal subspaces one of which is the space of essential paths. Two simple examples are worked out with certain detail, the ADE graph A3 and the affine graph A[2]. For the first example the weak *-Hopf algebra coincides with the so called double triangle algebra. No use is made of Ocneanu’s cell calculus.
publishDate 2010
dc.date.none.fl_str_mv 2010-09
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/11336/9482
Trinchero, Roberto Carlos; Path on graphs and associated quantum groupoids; Unión Matemática Argentina; Revista de la Unión Matemática Argentina ; 51; 2; 9-2010; 147-170
0041-6932
1669-9637
url http://hdl.handle.net/11336/9482
identifier_str_mv Trinchero, Roberto Carlos; Path on graphs and associated quantum groupoids; Unión Matemática Argentina; Revista de la Unión Matemática Argentina ; 51; 2; 9-2010; 147-170
0041-6932
1669-9637
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol51
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
dc.publisher.none.fl_str_mv Unión Matemática Argentina
publisher.none.fl_str_mv Unión Matemática Argentina
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 13.22299

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