English

Multiparameter quantum groups, bosonizations and cocycle deformations

Quantum Algebra 2016-03-14 v3

Abstract

We describe quantum groups given by multiparametric deformations of enveloping algebras of Kac-Moody algebras as a family of pointed Hopf algebras introduced by Andruskiewitsch and Schneider associated to a generalized Cartan matrix. We show that under some assumptions, these Hopf algebras depend only on one parameter on each connected component of the Dynkin diagram, up to a cocycle deformation. In particular, we obtain in this way a known result of Hu, Pei and Rosso.

Keywords

Cite

@article{arxiv.1406.2561,
  title  = {Multiparameter quantum groups, bosonizations and cocycle deformations},
  author = {Gaston Andres Garcia},
  journal= {arXiv preprint arXiv:1406.2561},
  year   = {2016}
}

Comments

17 pages. This version: major revision. Abstract is changed, preliminaries are extended and old Section 2 is now merged into the preliminaries. This version is suppose to be more friendly to non-experts. Comments are welcome!

R2 v1 2026-06-22T04:35:04.774Z