CoKahler and Cosymplectic Hom-Lie Algebras

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

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.20, sa.2, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s00009-023-02282-9
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: Hom-Lie group, Hom-Lie algebra, coKahler structure, cosymplectic structure, DEFORMATIONS
  • Atatürk Üniversitesi Adresli: Evet

Özet

The purpose of this study is to introduce the (almost) cosymplectic Hom-Lie algebras and to show that these Hom-Lie algebras and symplectic Hom-Lie algebras are related to each other. We also describe the notion of the almost coKahler structures on Hom-Lie algebras and show that they are related to almost Kahler structures. The properties of the curvature tensor of such structures are presented in this study. eta-Einstein almost coKahler Hom-Lie algebras are described as well. We give the notions of Hom-eta-parallel and Hom-cyclic parallel. Finally, some conditions for an almost Kahler structure induced by an almost coKahler Hom-Lie algebra to be totally geodesic are given.