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

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 leadi...

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Bibliographic Details
Published in:Communications in algebra 2021-08, Vol.49 (10), p.4469-4490
Main Authors: Abchir, H., Ait Brik, Ilham, Boucetta, Mohamed
Format: Article
Language:English
Subjects:
Algebra
k-Symplectic Lie algebras
left symmetric algebras
Lie groups
Mathematical analysis
R-matrices
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Summary: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 and all the six dimensional 2-para-Kähler Lie algebras.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2021.1922697