Year 2021, Volume 50 , Issue 3, Pages 845 - 854 2021-06-07

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

Tuuelbay KURBANBAEV [1] , Rustam TURDİBAEV [2]


All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.
Leibniz algebra, Leibniz algebra bimodule, Finite-dimensional Leibniz algebra
  • [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.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-9963-872X
Author: Tuuelbay KURBANBAEV (Primary Author)
Institution: Karakalpak State University
Country: Uzbekistan


Orcid: 0000-0002-0706-8169
Author: Rustam TURDİBAEV
Institution: Uzbekistan Academy of Sciences University
Country: Uzbekistan


Supporting Institution Karakalpak State University
Project Number ОТ-4-27
Dates

Publication Date : June 7, 2021

Bibtex @research article { hujms788994, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2021}, volume = {50}, pages = {845 - 854}, doi = {10.15672/hujms.788994}, title = {Finite-dimensional Leibniz algebra representations of \$\\mathfrak\{sl\}\_2\$}, key = {cite}, author = {Kurbanbaev, Tuuelbay and Turdibaev, Rustam} }
APA Kurbanbaev, T , Turdibaev, R . (2021). Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$ . Hacettepe Journal of Mathematics and Statistics , 50 (3) , 845-854 . DOI: 10.15672/hujms.788994
MLA Kurbanbaev, T , Turdibaev, R . "Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$" . Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 845-854 <https://dergipark.org.tr/en/pub/hujms/issue/62731/788994>
Chicago Kurbanbaev, T , Turdibaev, R . "Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$". Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 845-854
RIS TY - JOUR T1 - Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$ AU - Tuuelbay Kurbanbaev , Rustam Turdibaev Y1 - 2021 PY - 2021 N1 - doi: 10.15672/hujms.788994 DO - 10.15672/hujms.788994 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 845 EP - 854 VL - 50 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.788994 UR - https://doi.org/10.15672/hujms.788994 Y2 - 2021 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$ %A Tuuelbay Kurbanbaev , Rustam Turdibaev %T Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$ %D 2021 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 50 %N 3 %R doi: 10.15672/hujms.788994 %U 10.15672/hujms.788994
ISNAD Kurbanbaev, Tuuelbay , Turdibaev, Rustam . "Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$". Hacettepe Journal of Mathematics and Statistics 50 / 3 (June 2021): 845-854 . https://doi.org/10.15672/hujms.788994
AMA Kurbanbaev T , Turdibaev R . Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 845-854.
Vancouver Kurbanbaev T , Turdibaev R . Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 845-854.
IEEE T. Kurbanbaev and R. Turdibaev , "Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$", Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, pp. 845-854, Jun. 2021, doi:10.15672/hujms.788994