Kähler-Norden structures on Hom-Lie groups and Hom-Lie algebras

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

Hacettepe Journal of Mathematics and Statistics, cilt.54, sa.1, ss.213-236, 2025 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 54 Sayı: 1
• Basım Tarihi: 2025
• Doi Numarası: 10.15672/hujms.1344687
• Dergi Adı: Hacettepe Journal of Mathematics and Statistics
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
• Sayfa Sayıları: ss.213-236
• Anahtar Kelimeler: holomorphic Norden structure, Hom-Lie algebra, Hom-Lie group, Kähler-Norden structure
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• Atatürk Üniversitesi Adresli: Evet

Özet

The aim of this paper is to describe two geometric notions, holomorphic Norden structures and Kähler-Norden structures on Hom-Lie groups, and study their relationships in the left invariant setting. We study Kähler-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.