To each solution of the Yang-Baxter equation one may associate a quadratic algebra over a field, called the YB-algebra, encoding certain information about the solution. It is known that YB-algebras of finite non-degenerate solutions are (two-sided) Noetherian, PI and of finite Gelfand-Kirillov dimension. If the solution is additionally involutive then the corresponding YB-algebra shares many other properties with polynomial algebras in commuting variables (e.g., it is a Cohen-Macaulay domain of finite global dimension). The aim of this talk is to explain the intriguing relationship between ring-theoretical and homological properties of YB-algebras and properties of the corresponding solutions of the Yang-Baxter equation. The main focus is on when such algebras are Noetherian, (semi)prime and representable.
The talk is based on a joint work with I. Colazzo, E. Jespers and A. Van Antwerpen.
This video is part of the European Non-Associative Algebra Seminar series.
