Dehornoy's class and Sylows for set-theoretical solutions of the Yang-Baxter equation

2023/02/06 by Feingesicht, Edouard
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2302.02652

Abstract

We explain how the germ of the structure group of a cycle set decomposes as a product of its Sylow-subgroups, and how this process can be reversed to construct cycle sets from ones with coprime classes. We study Dehornoy's class associated to a cycle set, and conjecture a bound that we prove in a specific case. We combine the use of braces and a monomial representation, in particular to answer a question by Dehornoy on retrieving the Garside structure without a theorem of Rump, while also retrieving said theorem.

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