Cargando…

Twisting all the way: from algebras to morphisms and connections

Given a Hopf algebra H and an algebra A that is an H-module algebra we consider the category of left H-modules and A-bimodules, where morphisms are just right A-linear maps (not necessarily H-equivariant). Given a twist F of H we then quantize (deform) H to H^F, A to A_\star and correspondingly the...

Descripción completa

Detalles Bibliográficos
Autor principal: Aschieri, Paolo
Lenguaje:eng
Publicado: 2012
Materias:
Acceso en línea:https://dx.doi.org/10.1142/S201019451200668X
http://cds.cern.ch/record/1483147
_version_ 1780926016908165120
author Aschieri, Paolo
author_facet Aschieri, Paolo
author_sort Aschieri, Paolo
collection CERN
description Given a Hopf algebra H and an algebra A that is an H-module algebra we consider the category of left H-modules and A-bimodules, where morphisms are just right A-linear maps (not necessarily H-equivariant). Given a twist F of H we then quantize (deform) H to H^F, A to A_\star and correspondingly the category of left H-modules and A-bimodules to the category of left H^F-modules and A_\star-bimodules. If we consider a quasitriangular Hopf algebra H, a quasi-commutative algebra A and quasi-commutative A-bimodules, we can further construct and study tensor products over A of modules and of morphisms, and their twist quantization. This study leads to the definition of arbitrary (i.e., not necessarily H-equivariant) connections on quasi-commutative A-bimodules, to extend these connections to tensor product modules and to quantize them to A_\star-bimodule connections. Their curvatures and those on tensor product modules are also determined.
id cern-1483147
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2012
record_format invenio
spelling cern-14831472023-03-14T18:29:56Zdoi:10.1142/S201019451200668Xhttp://cds.cern.ch/record/1483147engAschieri, PaoloTwisting all the way: from algebras to morphisms and connectionsMathematical Physics and MathematicsGiven a Hopf algebra H and an algebra A that is an H-module algebra we consider the category of left H-modules and A-bimodules, where morphisms are just right A-linear maps (not necessarily H-equivariant). Given a twist F of H we then quantize (deform) H to H^F, A to A_\star and correspondingly the category of left H-modules and A-bimodules to the category of left H^F-modules and A_\star-bimodules. If we consider a quasitriangular Hopf algebra H, a quasi-commutative algebra A and quasi-commutative A-bimodules, we can further construct and study tensor products over A of modules and of morphisms, and their twist quantization. This study leads to the definition of arbitrary (i.e., not necessarily H-equivariant) connections on quasi-commutative A-bimodules, to extend these connections to tensor product modules and to quantize them to A_\star-bimodule connections. Their curvatures and those on tensor product modules are also determined.Given a Hopf algebra H and an algebra A that is an H-module algebra we consider the category of left H-modules and A-bimodules, where morphisms are just right A-linear maps (not necessarily H-equivariant). Given a twist F of H we then quantize (deform) H to H^F, A to A_\star and correspondingly the category of left H-modules and A-bimodules to the category of left H^F-modules and A_\star-bimodules. If we consider a quasitriangular Hopf algebra H, a quasi-commutative algebra A and quasi-commutative A-bimodules, we can further construct and study tensor products over A of modules and of morphisms, and their twist quantization. This study leads to the definition of arbitrary (i.e., not necessarily H-equivariant) connections on quasi-commutative A-bimodules, to extend these connections to tensor product modules and to quantize them to A_\star-bimodule connections. Their curvatures and those on tensor product modules are also determined.arXiv:1210.1143CERN-PH-TH-2012-064CERN-PH-TH-2012-064oai:cds.cern.ch:14831472012-10-04
spellingShingle Mathematical Physics and Mathematics
Aschieri, Paolo
Twisting all the way: from algebras to morphisms and connections
title Twisting all the way: from algebras to morphisms and connections
title_full Twisting all the way: from algebras to morphisms and connections
title_fullStr Twisting all the way: from algebras to morphisms and connections
title_full_unstemmed Twisting all the way: from algebras to morphisms and connections
title_short Twisting all the way: from algebras to morphisms and connections
title_sort twisting all the way: from algebras to morphisms and connections
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1142/S201019451200668X
http://cds.cern.ch/record/1483147
work_keys_str_mv AT aschieripaolo twistingallthewayfromalgebrastomorphismsandconnections