Geometrical approach on set theoretical solutions of Yang-Baxter equation in Lie algebras

Şerife Nur BOZDAĞ; Ibrahim Senturk

doi:10.26637/mjm1003/006

Abstract

In this paper, we handle set-theoretical solutions of Yang-Baxter equation and Lyubashenko set theoretical solutions in Lie algebras. We present a new commutative binary operation on these structures, and we obtain new set theoretical solutions including this operation by using property of commutativity of it. Also, we show that some set theoretical solutions of Yang-Baxter equation corresponds to the Lyubashenko set theoretical solutions on these structures. Additionally, we give some relations to verify set theoretical solution of Yang-Baxter equation. Moreover, we put an interpretation for these solutions from the point of geometrical view in Euclidean space, Minkowski space and differentiable manifolds by using Lie algebras.

Keywords:

Yang-Baxter equation, Lyubashenko solution, Lie algebras, Set theoretical solutions, Differentiable manifolds, Minkowski space

Mathematics Subject Classification:

16T25, 17B66, 53C99, 81R99

Authors Imprint References Funding Related Articles Downloads

Şerife Nur BOZDAĞ Faculty of Science, Department of Mathematics, Ege University, ˙ Izmir, Turkey. https://orcid.org/0000-0002-9651-7834
Ibrahim Senturk Faculty of Science, Department of Mathematics, Ege University, ˙ Izmir, Turkey.

Pages: 237-256
Date Published: 01-07-2022
Vol. 10 No. 03 (2022): Malaya Journal of Matematik (MJM)

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