Indecomposable set-theoretical solutions to the Yang--Baxter equation on a set of size $pq$

Carsten Dietzel; Raul Sastriques Guardiola

Indecomposable set-theoretical solutions to the Yang--Baxter equation on a set of size $pq$

Quantum Algebra 2023-06-06 v2 Group Theory Rings and Algebras

Authors: Carsten Dietzel , Raul Sastriques Guardiola

Abstract

Let $p$ and $q$ be different prime numbers. Using recent results of Ced\'o and Okni\'nski, we describe isomorphism classes of indecomposable set-theoretic solutions to the Yang--Baxter equation of cardinality $pq$ .

Keywords

yang-baxter equation set-theoretic solution indecomposable prime numbers isomorphism classes

Cite

@article{arxiv.2302.04636,
  title  = {Indecomposable set-theoretical solutions to the Yang--Baxter equation on a set of size $pq$},
  author = {Carsten Dietzel and Raul Sastriques Guardiola},
  journal= {arXiv preprint arXiv:2302.04636},
  year   = {2023}
}

Comments

Results are already contained in the paper [Jedli\^cka, Premysl; Pilitowska, Agata; Indecomposable involutive solutions of the Yang-Baxter equation of multipermutation level 2 with non-abelian permutation group. J. Combin. Theory Ser. A 197 (2023), Paper No. 105753, 35 pp.]

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