Generalized virtual braid groups, quasi-shuffle product and quantum groups
Quantum Algebra
2015-08-11 v1 Combinatorics
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.1311.3466,
title = {Generalized virtual braid groups, quasi-shuffle product and quantum groups},
author = {Xin Fang},
journal= {arXiv preprint arXiv:1311.3466},
year = {2015}
}
Comments
10 pages