2021/10/05 by Marco Castelli, Castelli, Marco
Mathematics · Physics and Astronomy · #16T25 #20E22 #20N02 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2110.01912
openalex publication_date 2021/10/05 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In the first part of this paper, we investigate the retraction of finite uniconnected involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation by means of left braces, giving a precise description in some cases. In the core of the paper, we also use left braces to classify all the uniconnected involutive non-degenerate set-theoretic solutions having odd size and a Z-group permutation group. As an application, we classify all the uniconnected involutive non-degenerate solutions having odd square-free size.