Solutions of Yang Baxter equation of mock-Lie algebras and related Rota Baxter algebras

Amir Baklouti

doi:10.3390/IOCMA2023-14397

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Solutions of Yang Baxter equation of mock-Lie algebras and related Rota Baxter algebras

Amir Baklouti

¹ Umm Al-Qura university

Academic Editor: Inna Huang

Published: 28 April 2023 by MDPI in The 1st International Online Conference on Mathematics and Applications session Algebra and Geometry with Applications to Related Fields

https://doi.org/10.3390/IOCMA2023-14397

Abstract:

We study the structure of symplectic mock-Lie algebras, and we give a necessary and sufficient condition to construct a symplectic Lie algebra, starting from a symplectic mock Lie algebra. Moreover, we investigate the equivalence between the existence of a symplectic form on a mock-Lie algebra and the existence of a solution of the Yang-Baxter equation. Finally, we conclude the work with the salient results and discussion.

Keywords: mock-Lie algebras; Yang-Baxter equation; Rota Baxter equation; symplectic structures

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Amir Baklouti