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arXiv · 2010.15815

On $k$-para-Kähler Lie algebras a subclass of $k$-symplectic Lie algebras

Hamid Abchir·Ilham Ait Brik·Mohamed Boucetta
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Abstract

$k$-Para-Kähler Lie algebras are a generalization of para-Kähler Lie algebras $(k=1)$ and constitute a subclass of $k$-symplectic Lie algebras. In this paper, we show that the characterization of para-Kähler Lie algebras as left symmetric bialgebras can be generalized to $k$-para-Kähler Lie algebras leading to the introduction of two new structures which are different but both generalize the notion of left symmetric algebra. This permits also the introduction of generalized $S$-matrices. We determine then all the $k$-symplectic Lie algebras of dimension $(k+1)$ and all the six dimensional 2-para-Kähler Lie algebras.

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Hamid Abchir, Ilham Ait Brik, Mohamed Boucetta. 2020-10-29. On $k$-para-Kähler Lie algebras a subclass of $k$-symplectic Lie algebras. https://arxiv.org/abs/2010.15815

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