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arXiv · 1311.3466

Generalized virtual braid groups, quasi-shuffle product and quantum groups

Xin Fang
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Abstract

We introduce in this paper the generalized virtual braid group on n strands GVB_n, generalizing simultaneously the braid groups and their virtual versions. A Mastumoto-Tits type section lifting shuffles in a symmetric group S_n to the monoid associated to GVB_n is constructed, which is then applied to characterize the quantum quasi-shuffle product. A family of representations of GVB_n is constructed using quantum groups.

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Xin Fang. 2013-11-14. Generalized virtual braid groups, quasi-shuffle product and quantum groups. https://arxiv.org/abs/1311.3466

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