Simple solutions of the Yang-Baxter equation of cardinality $p^n$
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 $|X| = p^n$ 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.
Fields of Study & Subjects
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Publicacions Matemàtiques
- Volume
- 70
- Pages
- 303–313
- Publication date
- 17 June 2026
- Language
- EN