Geometrical approach on set theoretical solutions of Yang-Baxter equation in Lie algebras
Articles > Article · 2022
Authors: İbrahim ŞENTÜRK, Şerife Nur BOZDAĞ
Malaya Journal of Matematik, Refereed Journals of Other Institutions, International, MathSciNet, 2022, vol 10, pp 237-256
DOI: 10.26637/mjm1003/006
Summary
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.