Speaker: Valeriy Bardakov (Sobolev Institute of Mathematics, Novosibirsk)
Date and time: 30.11.2022, 17:00 (GMT +03:00)
Title: REPRESENTATIONS OF THE VIRTUAL BRAID GROUP AND THE YANG-BAXTER EQUATION
Abstract: It is well known that a solution for the Yang–Baxter equation (YBE) or that is equivalent for the braid equation (BE) gives a representation of the braid group Bn. In this talk I explain a connection between YBE and representations of the virtual braid group VBn. In particular, I show that any solution (X, R) for the Yang–Baxter equation with invertible R defines a representation of the virtual pure braid group VPn, for any n ≥ 2, into Aut(X⊗n) for linear solution and into Sym(Xn) for set-theoretic solution. Any solution of the BE with invertible R gives a representation of a normal subgroup Hn of VBn. As a consequence of two these results we get that any invertible solution for the BE or YBE gives a representation of VBn.
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