Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 527
On k-para-K¨ahler Lie algebras a subclass of k-symplectic Lie algebras
Ilham Ait Brik, Hamid Abchir, Mohamed Boucetta
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
February 15, 2022
March 03, 2429
April 15, 2429

Abstract: k-para-Kähler Lie algebras are a generalization of para-Kähler Lie algebras (k = 1) and constitute a subclass of ksymplectic 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 dierent 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 ...