Work

Soluble skew left braces and soluble solutions of the Yang-Baxter equation

Year: 2024

Type: article

Abstract: The study of non-degenerate set-theoretic solutions of the Yang-Baxter equation calls for a deep understanding of the algebraic structure of a skew left brace. In this paper, the skew brace theoretical property of solubility is introduced and studied. It leads naturally to the notion of solubility of solutions of the Yang-Baxter equation. It turns out that soluble non-degenerate set-theoretic solutions are characterised by soluble skew left braces. The rich ideal structure of soluble skew left braces is also shown. A worked example showing the relevance of the brace theoretical property of solubility is also presented.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2024.109880

Authors: A. Ballester-Bolinches, R. Esteban-Romero, P. Jiménez-Seral, V. Pérez-Calabuig

Institutions: Universitat de València, Guangdong University of Education, Universidad de Zaragoza

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,510

OpenAlex ID: W4401520998

FWCI: 8.718

Cites: 27

Cited by: 8

Related to: 10