Abstract

The 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 construction of relative Rota-Baxter operators, using known Rota-Baxter operators, describe some of these operators on 2-step nilpotent groups and construct some solutions to the Yang-Baxter equation on 2-step nilpotent groups. This is joint work with T. Kozlovskaya, P. Sokolov, K. Zimireva, and M. Zonov.