SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 3

Complex and Kähler structures on hom-Lie algebras

Esmaeil Peyghan(Arak University)0000-0002-2713-6253
Leila Nourmohammadifar(Arak University)0000-0002-8772-4460
Pages
—
Publication Date
2020-06-02
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we describe all two-dimension non-abelian Kähler hom-Lie algebra and also it is shown that there does not exist a non-abelian Kähler proper hom-Lie algebra of dimension two.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:(Almost) Complex and Hermitian structures on hom-Lie algebras are introduced and some examples of these structures are presented.
📊
Key Findings & Data:We study the complexification of hom-Lie algebras.
💡
Conclusion & Impact:Finally, we describe all two-dimension non-abelian Kähler hom-Lie algebra and also it is shown that there does not exist a non-abelian Kähler proper hom-Lie algebra of dimension two.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Proper hom-Lie algebra · almost Hermitian structure · hom-Levi-Civita product

Abstract

(Almost) Complex and Hermitian structures on hom-Lie algebras are introduced and some examples of these structures are presented. We study the complexification of hom-Lie algebras. Also, the notion of Kähler hom-Lie algebras is introduced and then using a Kähler hom-Lie algebra, we present a phase space. Finally, we describe all two-dimension non-abelian Kähler hom-Lie algebra and also it is shown that there does not exist a non-abelian Kähler proper hom-Lie algebra of dimension two.

🔖

Cite This Article

Peyghan, E., Nourmohammadifar, L. (2020). Complex and Kähler structures on hom-Lie algebras. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 3. https://doi.org/10.15672/hujms.488823

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. A. Andrada, M.L. Barberis, and I. Dotti, Classification of abelian complex structures on 6-dimensional Lie algebras, J. London Math. Soc. 83, 232–255, 2011.
  2. A. Andrada and S. Salamon, Complex product structures on Lie algebras, Forum Math. 17, 261–295, 2005.
  3. S. Benayadi and A. Makhlouf, Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms, J. Math. Phys. 76, 38–60, 2014.
  4. G. Calvaruso and A. Fino, Five-dimensional K-contact Lie algebras, Monatsh. Math. 167 (1), 35–59, 2012.
  5. J. Hartwig, D. Larsson, and S. Silvestrov, Deformations of Lie algebras using σ- derivations, J. Algebra 295, 314–361, 2006.
  6. N. Hu, q-Witt algebras, q-Lie algebras, q-holomorph structure and representations, Algebra Colloq., 6 (1), 51–70, 1999.
  7. J. Jiang, S.K. Mishra, and Y. Sheng, Hom-Lie algebras and hom-Lie groups, integration and differentiation, arXiv:1904.06515.
  8. D. Larsson and S. Silvestrov, Quasi-hom-Lie algebras, central extensions and 2- cocycle-like identities, J. Algebra 288, 321–344, 2005.
  9. A. Makhlouf and S.D. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl. 2 (2), 51–64, 2008.
  10. A. Makhlouf and S D. Silvestrov, Notes on formal deformations of hom-associative and hom-Lie algebras, Forum Math. 22, 715–759, 2010.
  11. A. Makhlouf and D. Yau, Rota-baxter hom-lie admissible algebras, Comm. Algebra. 42, 1231–1257, 2014.
  12. E. Peyghan and L. Nourmohammadifar, Para-Kähler hom-Lie algebras, J. Algebra Appl. 18 (3), 1950044, 2019.
  13. E. Peyghan and L. Nourmohammadifar, Para-Kähler hom-Lie algebras of dimension 2, submitted.
  14. Y. Sheng and C. Bai, A new approach to hom-Lie bialgebras, J. Algebra 399, 232–250, 2014.
  15. Y. Sheng and D. Chen, Hom-Lie 2-algebras, J. Algebra 376, 174–195, 2013.
  16. Z. Xiong, Hom-Lie groups of a class of hom-Lie algebra, arXiv:1810.07881.