Structure monoid of left non-degenerate solutions to the Yang—Baxter equation
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 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 as a regular submonoid in the semidirect product , we will prove that 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 and we will discuss the positive answer to a conjecture of Gateva–Ivanova on cancellativity of .