Multiparameter quantum groups, bosonizations and cocycle deformations

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.

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!

References in corpus (4)

• Cohomology for quantum groups via the geometry of the nullcone
• Construction of quantized enveloping algebras by cocycle deformation
• The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
• Pointed Hopf algebras as cocycle deformations

Cited by in corpus (1)

• Formal multiparameter quantum groups, deformations and specializations