Bijective set-theoretic solutions of the Pentagon Equation

Abstract: The pentagon equation appears in various contexts: for example, any finite-dimensional Hopf algebra is characterised by an invertible solution of the Pentagon Equation, or an arrow is a fusion operator for a fixed braided monoidal category if it satisfies the Pentagon Equation. This talk, based on joint work with E. Jespers and Ł. Kubat, will introduce the basic properties of set-theoretic solutions of the Pentagon Equation, present a complete description of all involutive solutions, and discuss when two involutive solutions are isomorphic.

group theoryrings and algebras

Audience: researchers in the topic

Al@Bicocca take-away