Preprint Communication Version 1 Preserved in Portico This version is not peer-reviewed

Perspectives on the Yang-Baxter Equation in Bck-Algebras

Version 1 : Received: 18 February 2021 / Approved: 18 February 2021 / Online: 18 February 2021 (17:26:17 CET)

How to cite: Nichita, F.; Oner, T.; KALKAN, T.; Senturk, I.; Terziler, M. Perspectives on the Yang-Baxter Equation in Bck-Algebras. Preprints 2021, 2021020425. https://doi.org/10.20944/preprints202102.0425.v1 Nichita, F.; Oner, T.; KALKAN, T.; Senturk, I.; Terziler, M. Perspectives on the Yang-Baxter Equation in Bck-Algebras. Preprints 2021, 2021020425. https://doi.org/10.20944/preprints202102.0425.v1

Abstract

We present set-theoretical solutions of the Yang-Baxter equation in BCK–algebras. Some solutions in BCK−algebras are not solutions in other structures (such as MV −algebras). Related to our investigations we also consider some new structures: Boolean coalgebras and a unified braid condition – quantum Yang-Baxter equation. Finally, we will see how poetry has accompanied the development / history of the Yang–Baxter equation.

Keywords

BCK-algebras; Yang-Baxter Equation; Quasi-negation operator; Boolean coalgebras; poetry

Subject

Computer Science and Mathematics, Mathematics

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