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arXiv · 2002.03436

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

E. Peyghan·L. Nourmohammadifar·A. Makhlouf·A. Gezer
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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.

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E. Peyghan, L. Nourmohammadifar, A. Makhlouf, A. Gezer. 2020-02-09. K\"{a}hler-Norden structures on Hom-Lie group and Hom-Lie algebras. https://arxiv.org/abs/2002.03436

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