Yang-Baxter equation in median algebras


ÖNER T. , Katican T., Saeid A. B.

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, vol.70, no.1, pp.79-95, 2021 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1007/s12215-020-00486-6
  • Title of Journal : RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO
  • Page Numbers: pp.79-95
  • Keywords: Yang-Baxter equation, Median algebra, Ternary algebra

Abstract

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.