On the indecomposable involutive set-theoretic solutions of the\n Yang-Baxter equation of prime-power size

2019/11/13 by Marco Castelli, Castelli, Marco, Giuseppina Pinto +3
Mathematics · #2010: 16T25 #20E22 #20F16 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Quantum Algebra (math.QA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1911.05457

openalex publication_date 2019/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a method to construct all the indecomposable involutive\nset-theoretic solutions of the Yang-Baxter equation with a prime-power number\nof elements and cyclic permutation group. Moreover, we give a complete\nclassification of the indecomposable ones having abelian permutation group and\ncardinality pq (where p and q are prime numbers not necessarily\ndistinct).\n

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