Multiparameter quantum groups, bosonizations and cocycle deformations

Abstract

The multiparameter quantized enveloping algebras Uq(gA) constructed by Pei, Hu and Rosso [Quantum affine algebras, extended affine Lie algebras, and their applications, 145–171, Amer. Math. Soc., Providence, 2010] are presented as the pointed Hopf algebras Ue(Dred, `) defined by Andruskiewitsch and Schneider [Ann. of Math. (2) 171 (2010), 375–417]. The result is applied to show that under a certain assumption Uq(gA) depends, up to cocycle deformation, on only one parameter in each connected component of the associated Dynkin diagram. In the special case that gA is simple, this was already shown by Pei, Hu and Rosso in an alternative way.