Affiliation:
1. Department of Mathematics, Nanjing Agricultural University, Nanjing 210095, China
Abstract
In this paper, we introduce the concept of Rota–Baxter skew braces, and provide classifications of Rota–Baxter operators on various skew braces, such as (Z,+,∘) and (Z/(4),+,∘). We also present a necessary and sufficient condition for a skew brace to be a co-inverse skew brace. Additionally, we describe some constructions of Rota–Baxter quasiskew braces, and demonstrate that every Rota–Baxter skew brace can induce a quasigroup and a Rota–Baxter quasiskew brace.
Reference38 articles.
1. Braces, radical rings, and the quantum Yang–Baxter equation;Rump;J. Algebra,2007
2. Classification of braces of order p3;Bachiller;J. Pure Appl. Algebra,2015
3. Extensions, matched products, and simple braces;Bachiller;J. Pure Appl. Algebra,2018
4. Trusses: Between braces and rings;Trans. Am. Math. Soc.,2019
5. Braces and the Yang-Baxter equation;Jespers;Commun. Math. Phys.,2014