K\"{a}hler-Norden structures on Hom-Lie group and Hom-Lie algebras
Differential Geometry
2020-02-11 v1 Rings and Algebras
Abstract
In the present paper, we describe two geometric notions, holomorphic Norden structures and K\"{a}hler-Norden structures on Hom-Lie groups, and prove that on Hom-Lie groups in the left invariant setting, these structures are related to each other. 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
Cite
@article{arxiv.2002.03436,
title = {K\"{a}hler-Norden structures on Hom-Lie group and Hom-Lie algebras},
author = {E. Peyghan and L. Nourmohammadifar and A. Makhlouf and A. Gezer},
journal= {arXiv preprint arXiv:2002.03436},
year = {2020}
}