“Set-theoretic solutions of the Yang-Baxter equation and related associative structure”
Mercoledì 20 Aprile 2022, ore 16:30 - Aula 1C150 - Ilaria Colazzo (Università di Exeter)
The study of large classes of set-theoretic solutions can be reduced to the study of some associative algebraic objects, such as braces, skew braces, and semi-trusses. This talk will discuss the basic properties of skew braces and how these structures are related to non-degenerate bijective set-theoretic solutions to the Yang-Baxter equation. We will also discuss a possible extension of this theory to left non-degenerate solutions, not necessarily right non-degenerate. These new tools will allow us to prove that for a finite left non-degenerate solution being right non-degenerate is equivalent to being bijective.