Anna Zamojska-Dzienio (Warsaw University of Technology, Poland), Biracks and solutions of the Yang-Baxter equation

Tue, 12 Oct 2021, 1 pm MDT

The Yang-Baxter equation is a fundamental equation occurring in integrable models in statistical mechanics and quantum field theory. Description of all possible solutions seems to be extremely difficult and therefore there were some simplifications introduced (V.G. Drinfeld 1992).

Biracks are algebras studied in low-dimensional topology which are in a one-to-one correspondence with set-theoretical, non-degenerate solutions to the Yang-Baxter equation. The use of the language of biracks allows us to apply universal algebra tools. In this talk, we describe the generalized retraction relation on a birack which gives new classes of solutions.

This is joint work with Premysl Jedlicka and Agata Pilitowska.