AbstractThe Yang-Baxter equation is a fundamental equation in mathematical physics and statistical mechanics, it has connections with knot theory, braid theory and some algebraic systems. In my talk I recall the definition of the Yang-Baxter, Braid equation, skew brace and relative Rota-Baxter operators on group. Further we discuss connections between these objects, suggest some way for constru...
Abstract The study of R-matrices, matrix solutions of the spectral (parameter-dependent) Yang-Baxter equation, was a major motivation for the discovery of quantum groups. The quasitriangular structure of these bialgebras is the origin of large classes of R-matrices. The Yang-Baxter equation has a "twisted type-B/cylindrical" counterpart: the reflection equation. Its matrix solutions, known as K...