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arXiv · 2407.14913

Symplectic Leibniz algebras as a non-commutative version of symplectic Lie algebras

Fatima-Ezzahrae Abid·Mohamed Boucetta
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Abstract

We introduce symplectic left Leibniz algebras and symplectic right Leibniz algebras as generalizations of symplectic Lie algebras. These algebras possess a left symmetric product and are Lie-admissible. We describe completely symmetric Leibniz algebras that are symplectic as both left and right Leibniz algebras. Additionally, we show that symplectic left or right Leibniz algebras can be constructed from a symplectic Lie algebra and a vector space through a method that combines the double extension process and the $T^*$-extension. This approach allows us to generate a broad class of examples.

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Fatima-Ezzahrae Abid, Mohamed Boucetta. 2024-07-20. Symplectic Leibniz algebras as a non-commutative version of symplectic Lie algebras. https://arxiv.org/abs/2407.14913

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