A note on set-theoretic solutions of the Yang–Baxter equation
| Autor: | Agata Smoktunowicz |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Semidirect product
Ring (mathematics) Algebra and Number Theory Yang–Baxter equation Mathematics::Rings and Algebras 010102 general mathematics Mathematics - Rings and Algebras Jacobson radical Permutation group 01 natural sciences Brace Combinatorics Cardinality Rings and Algebras (math.RA) Mathematics::K-Theory and Homology Wreath product Mathematics::Category Theory Mathematics::Quantum Algebra 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Smoktunowicz, A 2018, ' A note on set-theoretic solutions of the Yang-Baxter equation ', Journal of Algebra, vol. 500, pp. 3-18 . https://doi.org/10.1016/j.jalgebra.2016.04.015 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2016.04.015 |
| Popis: | This paper shows that every finite non-degenerate involutive set theoretic solution (X,r) of the Yang-Baxter equation whose symmetric group has cardinality which a cube-free number is a multipermutation solution. Some properties of finite braces are also investigated (Theorems 3, 5 and 11). It is also shown that if A is a left brace whose cardinality is an odd number and (-a) b=-(ab) for all a, b A, then A is a two-sided brace and hence a Jacobson radical ring. It is also observed that the semidirect product and the wreath product of braces of a finite multipermutation level is a brace of a finite multipermutation level. Comment: Added a missing assumption in Theorem 5.2 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect