Ferran Cedó (Universitat Autònoma de Barcelona)
Indecomposable solutions of the Yang-Baxter equation of square-free cardinality
Abstract: Let $p_1,\dots,p_n$ be distinct prime numbers. Let $m_1,\dots,m_n$ be positive integers such that $m_1+\cdots+m_n>n$ . In previous joint work with J. Okni\'{n}ski, we proved that there exist simple involutive non-degenerate set-theoretic solutions $(X,r)$ of the Yang-Baxter equation with $|X|=p_1^{m_1}\cdots p_n^{m_n}$. A natural question is asked: If $n>1$, is there a simple involutive non-degenerate set-theoretic solution $(X,r)$ of the Yang-Baxter equation with $|X|=p_1\cdots p_n$?
In this talk, I will answer this question.
This is joint work with J. Okni\'{n}ski