K\"{a}hler-Norden structures on Hom-Lie groups and Hom-Lie algebras

Year 2024, Early Access, 1 - 24

E. Peyghan , Leila Nourmohammadifar , Abdenacer Makhlouf , Aydın Gezer

https://doi.org/10.15672/hujms.1344687

Abstract

The aim of this paper is to describe two geometric notions, holomorphic Norden structures and K\"{a}hler-Norden structures on Hom-Lie groups, and study their relationships in the left invariant setting. We study K\"{a}hler-Norden structures with abelian complex structures and give the curvature properties of holomorphic Norden structures on Hom-Lie groups. Finally, we show that any left-invariant holomorphic Hom-Lie group is a flat (holomorphic Norden Hom-Lie algebra carries a Hom-Left-symmetric algebra) if its left-invariant complex structure (complex structure) is abelian.

Keywords

Hom-Lie group, Hom-Lie algebra, holomorphic Norden structure, K\"{a}hler-Norden structure

References

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