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Self-distributive structures and reflections to set-theoretic solutions of the Yang–Baxter equation
- Speaker(s)
- Paola Stefanelli
- Affiliation
- University of Salento
- Language of the talk
- English
- Date
- Jan. 23, 2025, 12:15 p.m.
- Link
- https://uw-edu-pl.zoom.us/j/98300776179?pwd=rQz64ILq7lBS5bD1bsfHTPtqikClEG.1
- Information about the event
- referat online
- Seminar
- Seminar Algebra
The Yang–Baxter equation (YBE) is a fundamental equation of mathematical physics that has been extensively studied in the last few years. Alongside it, the reflection equation serves as a significant tool in the theory of quantum groups and integrable systems, which was first investigated in 1984 by Cherednik. In 2013, Caudrelier, Crampé, and Zhang formulated the set-theoretic version of this equation, and, later on, some new results were obtained mainly concerning involutive and non-degenerate solutions.
This talk aims to present a strategy for determining reflections to left non-degenerate set-theoretic solutions (X, r) of the YBE as provided in a joint work with A. Albano and M. Mazzotta, and obtained by examining the behaviour of these solutions with their derived solutions or, equivalently, with (left) self-distributive structures associated with them. Our approach is strongly motivated by a recent description of left non-degenerate solutions (X, r) in terms of Drinfel'd twist, namely, a family of automorphisms of the shelf associated with (X, r), which is obtained in a joint paper with A. Doikou and B. Rybołowicz.
