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

In this paper, we introduce the theory of Rota-Baxter operators on Clifford semigroups, useful tools for obtaining dual weak braces, i.e., triples (S, +, o) where (S, +) and (S, o) are Clifford semigroups such that ao(b + c) = aob -a +aoc and ao a- = -a + a, for all a, b, c is an element of 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.