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

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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).