Arne Van Antwerpen will be here on 16/17/18 May, visiting Olexandr Konovalov.
Arne will give a CIRCA seminar on the Wednesday afternoon, 4-5 in Theatre C.
Title: Multipermutation solutions of the Yang-Baxter equation and nilpotency of skew braces
Abstract: This talk will be based on joint work with Eric Jespers and Leandro Vendramin. The class of multipermutation solutions is a particularly interesting class of solutions of the celebrated Yang-Baxter equation (coming from mathematical physics) with a beautiful combinatorial structure. It was shown that this class corresponds to right nilpotent skew left braces of nilpotent type. In this talk we delve deeper into this class of skew left braces and identify the class of centrally nilpotent skew braces. We discuss that these behave very similar to nilpotent groups and will identify several possible central series for these objects. If time permits, we use this class to illustrate several other key concepts of skew left braces. The talk will be rife with examples and exciting open problems.