Complex and Kähler structures on hom-Lie algebras

Year 2020, Volume: 49 Issue: 3, 1039 - 1056, 02.06.2020

Esmaeil Peyghan , Leila Nourmohammadifar

https://doi.org/10.15672/hujms.488823

Cited By: 5

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

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