Twisted deformations vs. cocycle deformations for quantum groups

In this paper we study two deformation procedures for quantum groups: deformations by twists, that we call "comultiplication twisting", as they modify the coalgebra structure, while keeping the algebra one -- and deformations by 2-cocycle, that we call "multiplication twisting",...

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Autores principales: García, Gastón Andrés, Gavarini, Fabio
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2020
Materias:
Matemática
Structure (category theory)
Link (knot theory)
Type (model theory)
Algebraic structure
Pure mathematics
Simple (abstract algebra)
Coalgebra
Hopf algebra
Mathematics
Quantum
Realization (systems)
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/125209
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-125209
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Structure (category theory)
Link (knot theory)
Type (model theory)
Algebraic structure
Pure mathematics
Simple (abstract algebra)
Coalgebra
Hopf algebra
Mathematics
Quantum
Realization (systems)
spellingShingle Matemática
Structure (category theory)
Link (knot theory)
Type (model theory)
Algebraic structure
Pure mathematics
Simple (abstract algebra)
Coalgebra
Hopf algebra
Mathematics
Quantum
Realization (systems)
García, Gastón Andrés
Gavarini, Fabio
Twisted deformations vs. cocycle deformations for quantum groups
topic_facet Matemática
Structure (category theory)
Link (knot theory)
Type (model theory)
Algebraic structure
Pure mathematics
Simple (abstract algebra)
Coalgebra
Hopf algebra
Mathematics
Quantum
Realization (systems)
description In this paper we study two deformation procedures for quantum groups: deformations by twists, that we call "comultiplication twisting", as they modify the coalgebra structure, while keeping the algebra one -- and deformations by 2-cocycle, that we call "multiplication twisting", as they deform the algebra structure, but save the coalgebra one. We deal with quantum universal enveloping algebras, in short QUEA's, for which we accordingly consider those arising from twisted deformations (in short TwQUEA's) and those arising from 2-cocycle deformations, usually called multiparameter QUEA's (in short MpQUEA's). Up to technicalities, we show that the two deformation methods are equivalent, in that they eventually provide isomorphic outputs, which are deformations (of either kinds) of the "canonical", well-known one-parameter QUEA by Jimbo and Lusztig. It follows that the two notions of TwQUEA's and of MpQUEA's -- which, in Hopf algebra theoretical terms are naturally dual to each other -- actually coincide; thus, that there exists in fact only one type of "pluriparametric deformation" for QUEA's. In particular, the link between the realization of any such QUEA as a MpQUEA and that as a TwQUEA is just a (very simple, and rather explicit) change of presentation.
format Articulo
Preprint
author García, Gastón Andrés
Gavarini, Fabio
author_facet García, Gastón Andrés
Gavarini, Fabio
author_sort García, Gastón Andrés
title Twisted deformations vs. cocycle deformations for quantum groups
title_short Twisted deformations vs. cocycle deformations for quantum groups
title_full Twisted deformations vs. cocycle deformations for quantum groups
title_fullStr Twisted deformations vs. cocycle deformations for quantum groups
title_full_unstemmed Twisted deformations vs. cocycle deformations for quantum groups
title_sort twisted deformations vs. cocycle deformations for quantum groups
publishDate 2020
url http://sedici.unlp.edu.ar/handle/10915/125209
work_keys_str_mv AT garciagastonandres twisteddeformationsvscocycledeformationsforquantumgroups
AT gavarinifabio twisteddeformationsvscocycledeformationsforquantumgroups
bdutipo_str Repositorios
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