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 (S,+,∘) where (S,+) and (S,∘) are Clifford semigroups such that a∘(b+c)=a∘b−a+a∘c and a∘a−=−a+a, for all a,b,c∈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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