Simple solutions of the Yang-Baxter equation of cardinality pⁿ

2024/06/29 by Cedo, Ferran, Okninski, Jan
#16T25 #20B15 #20F16 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2407.07907

Abstract

For every prime number p and integer n>1, a simple, involutive, non-degenerate set-theoretic solution (X,r) of the Yang-Baxter equation of cardinality |X| = pⁿ is constructed. Furthermore, for every non-(square-free) positive integer m which is not the square of a prime number, a non-simple, indecomposable, irretractable, involutive, non-degenerate set-theoretic solution (X,r) of the Yang-Baxter equation of cardinality |X| = m is constructed. A recent question of Castelli on the existence of singular solutions of certain type is also answered affirmatively.

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