Gaussian solutions to the Yang--Baxter equation and their twists

Abstract

In this paper, we consider two explicit Gaussian solutions to the constant (or parameter-independent) quantum Yang--Baxter equation and produce the corresponding bialgebras using the Faddeev--Reshetikhin--Takhtajan construction (FRT). Additionally, we twist these two Gaussian solutions, via Zhang twists and corresponding 2-cocycle twists, to obtain solutions to the Yang--Baxter equation which are not necessarily Gaussian.

arXiv commentIn this version, theorem 4.3 has been updated and propositions 4.4 & 4.5 together with theorems 4.7 & 4.8 updated accordingly