Yang–Baxter equation in median algebras

In this paper, at first median algebras and the Yang–Baxter equation are studied, some of their properties are presented. After giving some solutions to the set-theoretical Yang–Baxter equation by using these properties, it is found a solution that is not usually a solution to the set-theoretical Ya...

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Bibliographic Details
Published in:Rendiconti del Circolo matematico di Palermo 2021-04, Vol.70 (1), p.79-95
Main Authors: Oner, Tahsin, Katican, Tugce, Borumand Saeid, Arsham
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Boolean algebra
Geometry
Mathematics
Mathematics and Statistics
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Summary:In this paper, at first median algebras and the Yang–Baxter equation are studied, some of their properties are presented. After giving some solutions to the set-theoretical Yang–Baxter equation by using these properties, it is found a solution that is not usually a solution to the set-theoretical Yang–Baxter equation in median algebras but it is the solution in Boolean algebras.
ISSN:0009-725X
1973-4409
DOI:10.1007/s12215-020-00486-6