- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 3
- Complex and Kähler structures on hom-Lie algebras
Complex and Kähler structures on hom-Lie algebras
Authors : Esmaeil Peyghan, Leila Nourmohammadifar
Pages : 1039-1056
Doi:10.15672/hujms.488823
View : 11 | Download : 6
Publication Date : 2020-06-02
Article Type : Research
Abstract :(Almost) Complex and Hermitian structures on hom-Lie algebras are introduced and some examples of these structures are presented. We study the complexification of hom-Lie algebras. Also, the notion of Kähler hom-Lie algebras is introduced and then using a Kähler hom-Lie algebra, we present a phase space. Finally, we describe all two-dimension non-abelian Kähler hom-Lie algebra and also it is shown that there does not exist a non-abelian Kähler proper hom-Lie algebra of dimension two.Keywords : Proper hom-Lie algebra, almost Hermitian structure, hom-Levi-Civita product, Kähler hom-Lie algebra, phase space