KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 3

Complex and Kähler structures on hom-Lie

Esmaeil PEYGHAN
Leila NOURMOHAMMADİFAR
Sayfa
1039–1056
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:(Almost) Complex and Hermitian structures on hom-Lie algebras are introduced and someexamples of these structures are presented.
📊
Temel Bulgular & Veri:We study the complexification of hom-Liealgebras.
💡
Sonuç & Katkı:Finally, we describe all two-dimensionnon-abelian Kähler hom-Lie algebra and also it is shown that there does not exist a nonabelian Kähler proper hom-Lie algebra of dimension two.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

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

🔖

Bu Makaleye Atıf Yap

PEYGHAN, E., NOURMOHAMMADİFAR, L. (2022). Complex and Kähler structures on hom-Lie. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 3, 1039–1056. https://ajindex.com/articles/529697

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (13)

  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 σderivations, J. Algebra 295, 314–361, 2006. N. Hu, q-Witt algebras, q-Lie algebras, q-holomorph structure and representations, Algebra Colloq., 6 (1), 51–70, 1999.
  6. J. Jiang, S.K. Mishra, and Y. Sheng, Hom-Lie algebras and hom-Lie groups, integration and differentiation, arXiv:1904.06515. D. Larsson and S. Silvestrov, Quasi-hom-Lie algebras, central extensions and 2- cocycle-like identities, J. Algebra 288, 321–344, 2005.
  7. A. Makhlouf and S.D. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl. 2 (2), 51–64, 2008.
  8. A. Makhlouf and S D. Silvestrov, Notes on formal deformations of hom-associative and hom-Lie algebras, Forum Math. 22, 715–759, 2010.
  9. A. Makhlouf and D. Yau, Rota-baxter hom-lie admissible algebras, Comm. Algebra. 42, 1231–1257, 2014.
  10. E. Peyghan and L. Nourmohammadifar, Para-Kähler hom-Lie algebras, J. Algebra Appl. 18 (3), 1950044, 2019.
  11. E. Peyghan and L. Nourmohammadifar, Para-Kähler hom-Lie algebras of dimension 2, submitted. Y. Sheng and C. Bai, A new approach to hom-Lie bialgebras, J. Algebra 399, 232–250, 2014.
  12. Y. Sheng and D. Chen, Hom-Lie 2-algebras, J. Algebra 376, 174–195, 2013.
  13. Z. Xiong, Hom-Lie groups of a class of hom-Lie algebra, arXiv:1810.07881.