Involution semi-braces and the Yang-Baxter equation
Abstract
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
with
a semigroup and
an involution semigroup satisfying the relation
, for all
.
![(S,+,\cdot , ^\ast)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/6db998c791d2078b77d82e1989eed4f0.png)
![(S,+)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/2e96be47527a7857834c38e0d4eb2070.png)
![(S,\cdot , ^\ast)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/40ef748f3798fc13858814fceb34095b.png)
![a(b+c)=ab+a(a^\ast+c)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/7ffd39534c315d594acd29a8669a7ab1.png)
![a,b,c\in S](http://siba-ese.unile.it/plugins/generic/latexRender/cache/695aabe593f2ac6de18b7709813c5cf0.png)
DOI Code:
10.1285/i15900932v42n2p63
Keywords:
semi-brace; set-theoretical solution; Yang-Baxter equation; involution
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