## View abstract

### Session S16 - Quantum symmetries

Wednesday, July 14, 14:20 ~ 14:45 UTC-3

## Twisted deformations vs. cocycle deformations for quantum groups

### Gastón Andrés García

#### Universidad Nacional de La Plata, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak930c925fe0898c884090eee5fa9028fe').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy930c925fe0898c884090eee5fa9028fe = 'gg&#97;rc&#105;&#97;' + '&#64;'; addy930c925fe0898c884090eee5fa9028fe = addy930c925fe0898c884090eee5fa9028fe + 'm&#97;t&#101;' + '&#46;' + '&#117;nlp' + '&#46;' + '&#101;d&#117;' + '&#46;' + '&#97;r'; var addy_text930c925fe0898c884090eee5fa9028fe = 'gg&#97;rc&#105;&#97;' + '&#64;' + 'm&#97;t&#101;' + '&#46;' + '&#117;nlp' + '&#46;' + '&#101;d&#117;' + '&#46;' + '&#97;r';document.getElementById('cloak930c925fe0898c884090eee5fa9028fe').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy930c925fe0898c884090eee5fa9028fe + '\'>'+addy_text930c925fe0898c884090eee5fa9028fe+'<\/a>';

This talk is based on a joint project with F. Gavarini where we study different versions of multiparameter quantum groups. Here we focus on the study of quantum universal enveloping algebras, in short QUEA's, for which we 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. Thus, the two notions of TwQUEA's and of MpQUEA's --- which, in Hopf algebra theoretical terms are naturally dual to each other --- actually coincide.

Joint work with Fabio Gavarini (Univesitá degli studi di Roma "Tor Vergata").