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