Involution semi-braces and the Yang-Baxter equation


The main aim of this paper is to provide set-theoretical solutions of the Yang-Baxter equation that are not necessarily bijective. We use the new structure of involution semi-brace, that is a quadruple (S,+,\cdot , ^\ast) with (S,+) a semigroup and (S,\cdot , ^\ast) an involution semigroup satisfying the relation a(b+c)=ab+a(a^\ast+c), for all a,b,c\in S.

DOI Code: 10.1285/i15900932v42n2p63

Keywords: semi-brace; set-theoretical solution; Yang-Baxter equation; involution

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