Structure monoid of left non-degenerate solutions to the Yang

Structure monoid of left non-degenerate solutions to the Yang—Baxter equation

Postato il 18 febbraio 2019

February 20, 2019
11.00 – 13.00 – Aula Benvenuti
Arne Van Antwerper
(joint work with Eric Jespers and Lukasz Kubat)

In this talk we will discuss the structure monoid $M(X,r)$ of a finite left non-degenerate solution of the Yang–Baxter equation and its associated monoid algebra. Using a realization of Lebed and Vendramin of $M(X,r)$ as a regular submonoid in the semidirect product $A(X,r) \rtimes\textup{Sym}(X)$ , we will prove that $KM(X,r)$ is a finite module over a central affine subalgebra. In particular, it is a Noetherian PI-algebra of finite Gelfand–Kirillov dimension. Furthermore, we will discuss some results on prime ideals of $M(X,r)$ and we will discuss the positive answer to a conjecture of Gateva–Ivanova on cancellativity of $M(X,r)$ .