(CANCELLED) Braces and Set-theoretic Solutions of the Quantum Yang-Baxter and Reflections Equations

Robert Weston (Heriot-Watt University)

Tuesday 17th March, 2020 16:00-17:00 Maths 311B

Abstract

I will discuss the physical motivation for the study of set-theoretic solutions to the Yang-Baxter and reflections equations. I will then give a gentle introduction to 'braces'. A brace is a set X with 2 operations + and * such that (X,+) is an Abelian group, (X,*) is a group, and a*(b+c)=a*b+a*c-a. Such objects were introduced by Rump [07] in the context of understanding R-matrix solutions of the set-theoretic Yang-Baxter equation. I will introduce and give examples of braces and present the simple procedure for constructing the associated R-matrices. I will then construct examples of set theoretic solutions of the reflection equation. I will finish by showing how these solutions can be used to construct novel quantum integrable systems.

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