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arXiv · 2204.05004

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

Francesco Catino·Marzia Mazzotta·Paola Stefanelli
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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.

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Francesco Catino, Marzia Mazzotta, Paola Stefanelli. 2022-04-11. Rota-Baxter operators on Clifford semigroups and the Yang-Baxter equation. https://doi.org/10.1016/j.jalgebra.2023.02.013

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