Multi-parameter Quantum Groups and Quantum Shuffles, (I)

Details Multi-parameter Quantum Groups and Quantum Shuffles, (I) Multi-parameter Quantum Groups and Quantum Shuffles, (I)

2008-11-02

arxiv.org/abs/0811.0129v3

Contemporary Mathematics. vol. 506 (2010), 145-171

Mathematics

Quantum Algebra

31 pages. Contemp. Math. (to appear)

Scientific paper

In this article, we study the multi-parameter quantum groups defined by generators and relations associated with symmetrizable generalized Cartan matrices, together with their representations in the category $\mathcal O$. This presentation will be convenient for our later discussions. We present two explicit descriptions here: as a Hopf 2-cocycle deformation, and as the multi-parameter quantum shuffle realization of the positive part.

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