Mathematics of Computation· 2016Q1
Skew braces and the Yang–Baxter equation
- 299citations
- Q1SCImago
- 2016year
Short summary
A new non-commutative structure, generalizing Rump's braces, is introduced to study non-involutive solutions of the Yang–Baxter equation.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces non-commutative skew braces to generalize Rump's structure.
- Applies the new structure to study non-involutive, non-degenerate set-theoretic solutions of the Yang–Baxter equation.
- Develops an algorithm for enumerating and constructing small-sized braces.
- Creates a database of small-sized braces based on the algorithm.
AI-generated from the title and abstract; the full text is not read.
Abstract
Braces were introduced by Rump to study non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation. We generalize Rump’s braces to the non-commutative setting and use this new structure to study not necessarily involutive non-degenerate set-theoretical solutions of the Yang–Baxter equation. Based on results of Bachiller and Catino and Rizzo, we develop an algorithm to enumerate and construct classical and non-classical braces of small size up to isomorphism. This algorithm is used to produce a database of braces of small size. The paper contains several open problems, questions and conjectures.
The authors' abstract, as published at the source. Mathematics of Computation, 2016 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics