Rota-Baxter operators on Clifford semigroups and the Yang-Baxter equation

Abstract

In this paper, we introduce the theory of Rota-Baxter operators on Clifford semigroups, useful tools for obtaining dual weak braces, i.e., triples $\left(S,+,\circ \right)$ where $\left(S,+\right)$ and $\left(S,\circ \right)$ are Clifford semigroups such that $a\circ \left(b+c\right)=a\circ b-a+a\circ c$ and $a\circ a^{-}=-a+a$, for all $a,b,c\in S$. To each algebraic structure is associated a set-theoretic solution of the Yang-Baxter equation that has a behaviour near to the bijectivity and non-degeneracy. Drawing from the theory of Clifford semigroups, we provide methods for constructing dual weak braces and deepen some structural aspects, including the notion of ideal.

We improve Proposition 3. Accepted for publication in Journal of Algebra

References in corpus (2)

• Bi-skew braces and Hopf Galois structures
• Skew braces from Rota--Baxter operators: a cohomological characterisation and some examples

Cited by in corpus (6)

• Extensions and automorphisms of Rota-Baxter groups
• Relative Rota-Baxter groups and skew left braces
• Rota--Baxter operators and skew left brace structures over Heisenberg Group
• Schur multiplier and Schur covers of relative Rota-Baxter groups
• Solutions of the Yang-Baxter equation and strong semilattices of skew braces
• Cohomology and Extensions of Relative Rota-Baxter groups