# Multi-parameter Quantum Groups and Quantum Shuffles, I - Mathematics > Quantum Algebra

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

Author: Naihong Hu, Yufeng Pei, Marc Rosso

Source: https://arxiv.org/