Biracks and solutions of the Yang-Baxter equation

Abstract: 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.

computational complexitycategory theorylogic

Audience: researchers in the topic

PALS Panglobal Algebra and Logic Seminar

Series comments: The PALS seminar is a research and learning seminar organized by the algebra and logic research group of the Department of Mathematics at the University of Colorado at Boulder. The scope of the seminar includes all topics with links to algebra, logic, or their applications, like general algebra, logic, model theory, category theory, set theory, set-theoretic topology, or theoretical computer science. Please contact one of the organizers for the Zoom password, to join the mailing list or if you want to speak.