SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 3

Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$

Tuuelbay KURBANBAEV
Rustam TURDİBAEV
Pages
845–854
Publication Date
2021-06-07
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)

All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.
📊
Key Findings & Data:All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.
💡
Conclusion & Impact:All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Leibniz algebra · Leibniz algebra bimodule · Finite-dimensional Leibniz algebra

Abstract

All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.

🔖

Cite This Article

KURBANBAEV, T., TURDİBAEV, R. (2021). Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 845–854. https://ajindex.com/articles/669333

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. D. Barnes, Some Theorems on Leibniz algebras, Comm. Algebra, 39, 2463–2472, 2011
  2. A. Bloh, On a generalization of the concept of Lie algebra, Dokl. Akad. Nauk SSSR, 165, 471–473, 1965
  3. A.M. Bloh, A certain generalization of the concept of Lie algebra, Uch. Zap. Moskov. Gos. Ped. Inst. 375, 9–20, 1971 (in Russian)
  4. A.S. Dzhumadil’daev and A.S. Abdukassymova, Leibniz algebras in characteristic p, C.R.Acad.sci.Paris Ser. I Math. 332 (12), 1047–1052, 2001
  5. P. Gabriel, Unzerlegbare Darstellungen, I, Manuscripta Math. 6, 71–103, 1972
  6. N. Jacobson, Lie algebras, Interscience Publishers, Wiley, New York, 1962
  7. T. Kurbanbaev and R. Turdibaev, Some Leibniz bimodules of sl2, J. Algebra Appl. 19 (4), 2050064, 2020
  8. J.-L. Loday, Cyclic homology, Grundl. Math. Wiss. Bd. 301, Springer-Verlag, Berlin, 1992
  9. J.-L. Loday and T. Pirashvili, Universal enveloping algebras of Leibniz algebras and (co)homology, Math. Ann. 296, 139–158, 1993
  10. J.-L. Loday and T. Pirashvili, Leibniz representations of Lie algebras, J. Algebra, 181 (2), 414–425, 1996
  11. R. Martinez-Villa, Algebras Stably Equivalent to l-Hereditary, Springer Lecture Notes in Math., 832, pp. 396–431, Springer-Verlag, New York/Berlin, 1980.