Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 2

Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras

Pages
648–675
Publication Date
2022-10-18
DOI
—
🏛️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)

Derivations and central extensions of $\delta$-Bihom-Jordan-Lie algebras are also discussed as an application.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The purpose of this article is to study representations of $\delta$-Bihom-Jordan-Lie algebras.
📊
Key Findings & Data:In particular, adjoint representations, trivial representations, deformations, $T^\ast$-extensions of $\delta$-Bihom-Jordan-Lie algebras are studied in detail.
💡
Conclusion & Impact:Derivations and central extensions of $\delta$-Bihom-Jordan-Lie algebras are also discussed as an application.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:representations · derivations · deformations

Abstract

The purpose of this article is to study representations of $\delta$-Bihom-Jordan-Lie algebras. In particular, adjoint representations, trivial representations, deformations, $T^\ast$-extensions of $\delta$-Bihom-Jordan-Lie algebras are studied in detail. Derivations and central extensions of $\delta$-Bihom-Jordan-Lie algebras are also discussed as an application.

🔖

Cite This Article

Li, J., Chen, L., Hassine, A. B. (2022). Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 2, 648–675. https://ajindex.com/articles/529609

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (10)

  1. S. Benayadi and A. Makhlouf, Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms, J. Geom. Phys. 76, 38–60, 2014
  2. M. Bordemann, Nondegenerate invariant bilinear forms on nonassociative algebras, Acta Math. Univ. Comenian. (N.S.) 66 (2), 151–201, 1997
  3. Y. Cheng and H. Qi, Representations of Bihom-Lie algebras, arXiv:1610.04302
  4. G. Graziani, A. Makhlouf, C. Menini, and F. Panaite, Bihom-associative algebras, Bihom-Lie algebras and Bihom-bialgebras, SIGMA Symmetry Integrability Geom. Methods Appl. (11), Paper 086, 34 pp, 2015
  5. J. Hartwig, D. Larsson and S. Silvestrov, Deformations of Lie algebras using σ- derivations, J. Algebra 295 (2), 314–361, 2006
  6. A. Makhlouf and S. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl. 2 (2), 51–64, 2008
  7. S. Okubo and N. Kamiya, Jordan Lie superalgebra and Jordan Lie triple system, J. Algebra 198 (2), 388–411, 1997
  8. L. Qian, J. Zhou, and L. Chen, Engel’s theorem for Jordan-Lie algebras and its applications, Chinese Ann. Math. Ser. A 33 (5), 517–526, 2012 (in Chinese)
  9. S. Wang and S. Guo, Bihom-Lie superalgebra structures, arXiv:1610.02290
  10. J. Zhao, L. Chen, and L. Ma, Representations and $T^\ast$-extensions of Hom-Jordan-Lie Algebras, Comm. Algebra 44 (7), 2786–2812, 2016.