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

Tuuelbay Kurbanbaev; Rustam Turdibaev

doi:10.15672/hujms.788994

Araştırma Makalesi

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

Yıl 2021, Cilt: 50 Sayı: 3, 845 - 854, 07.06.2021

Tuuelbay Kurbanbaev , Rustam Turdibaev

https://doi.org/10.15672/hujms.788994

Öz

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

Anahtar Kelimeler

Leibniz algebra, Leibniz algebra bimodule, Finite-dimensional Leibniz algebra

Destekleyen Kurum

Karakalpak State University

Proje Numarası

ОТ-4-27

Kaynakça

[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.

Yıl 2021, Cilt: 50 Sayı: 3, 845 - 854, 07.06.2021

Tuuelbay Kurbanbaev , Rustam Turdibaev

https://doi.org/10.15672/hujms.788994

Öz

Proje Numarası

ОТ-4-27

Kaynakça

[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.

Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Matematik
Yazarlar	Tuuelbay Kurbanbaev 0000-0002-9963-872X Rustam Turdibaev 0000-0002-0706-8169
Proje Numarası	ОТ-4-27
Yayımlanma Tarihi	7 Haziran 2021
Yayımlandığı Sayı	Yıl 2021 Cilt: 50 Sayı: 3

Kaynak Göster

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. 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. Haziran 2021;50(3):845-854. doi:10.15672/hujms.788994
Chicago	Kurbanbaev, Tuuelbay, ve Rustam Turdibaev. “Finite-Dimensional Leibniz Algebra Representations of $\mathfrak{sl}_2$”. Hacettepe Journal of Mathematics and Statistics 50, sy. 3 (Haziran 2021): 845-54. https://doi.org/10.15672/hujms.788994.
EndNote	Kurbanbaev T, Turdibaev R (01 Haziran 2021) Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$. Hacettepe Journal of Mathematics and Statistics 50 3 845–854.
IEEE	T. Kurbanbaev ve R. Turdibaev, “Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 3, ss. 845–854, 2021, doi: 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 (Haziran 2021), 845-854. https://doi.org/10.15672/hujms.788994.
JAMA	Kurbanbaev T, Turdibaev R. Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$. Hacettepe Journal of Mathematics and Statistics. 2021;50:845–854.
MLA	Kurbanbaev, Tuuelbay ve Rustam Turdibaev. “Finite-Dimensional Leibniz Algebra Representations of $\mathfrak{sl}_2$”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 3, 2021, ss. 845-54, doi:10.15672/hujms.788994.
Vancouver	Kurbanbaev T, Turdibaev R. Finite-dimensional Leibniz algebra representations of $\mathfrak{sl}_2$. Hacettepe Journal of Mathematics and Statistics. 2021;50(3):845-54.