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BIPARTITE GRAPHS AND THE STRUCTURE OF FINITE-DIMENSIONAL SEMISIMPLE LEIBNIZ ALGEBRAS

Yıl 2019, Cilt: 26 Sayı: 26, 122 - 130, 11.07.2019
https://doi.org/10.24330/ieja.587009

Öz

Given a nite connected bipartite graph, fi nite-dimensional indecomposable
semisimple Leibniz algebras are constructed. Furthermore, any
fi nite-dimensional indecomposable semisimple Leibniz algebra admits a similar
construction.

Kaynakça

  • Sh. Ayupov, K. Kudaybergenov, B. Omirov and K. Zhao, Semisimple Leibniz algebras, their derivations and automorphisms, Linear Multilinear Algebra, (2019), accepted.
  • D. W. Barnes, On Levi's theorem for Leibniz algebras, Bull. Aust. Math. Soc., 86(2) (2012), 184-185.
  • A. Bloh, On a generalization of the concept of Lie algebra, Dokl. Akad. Nauk SSSR, 165 (1965), 471-473.
  • A. Ja. Bloh, A certain generalization of the concept of Lie algebra, Moskov. Gos. Ped. Inst. Ucen. Zap., 375 (1971), 9-20 (in Russian).
  • A. S. Dzhumadil'daev and S. A. Abdykassymova, Leibniz algebras in characteristic p, C. R. Acad. Sci. Paris Ser. I Math., 332(12) (2001), 1047-1052.
  • N. Jacobson, Lie Algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers, New York-London, 1962.
  • M. K. Kinyon and A.Weinstein, Leibniz algebras, Courant algebroids, and multiplications on reductive homogeneous spaces, Amer. J. Math., 123(3) (2001), 525-550.
  • K. Kudaybergenov, M. Ladra and B. Omirov, On Levi-Malcev theorem for Leibniz algebras, Linear Multilinear Algebra, 67(7) (2019), 1471-1482.
  • J.-L. Loday, Cyclic Homology, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 301, Springer- Verlag, Berlin, 1992.
  • J.-L. Loday, Une version non commutative des algebres de Lie: les algebres de Leibniz [A noncommutative version of Lie algebras: the Leibniz algebras], Enseign. Math., 39(2) (1993), 269-293.
  • G. Mason and G. Yamskulna, Leibniz algebras and Lie algebras, SIGMA Symmetry Integrability Geom. Methods Appl., 9 (2013), 063 (10 pp).
  • T. Pirashvili, On Leibniz homology, Ann. Inst. Fourier (Grenoble), 44(2) (1994), 401-411.
  • Z. X. Wan, Lie Algebras, International Series of Monographs in Pure and Applied Mathematics, Vol. 104, Pergamon Press, Oxford-New York-Toronto, Ont., 1975.
Yıl 2019, Cilt: 26 Sayı: 26, 122 - 130, 11.07.2019
https://doi.org/10.24330/ieja.587009

Öz

Kaynakça

  • Sh. Ayupov, K. Kudaybergenov, B. Omirov and K. Zhao, Semisimple Leibniz algebras, their derivations and automorphisms, Linear Multilinear Algebra, (2019), accepted.
  • D. W. Barnes, On Levi's theorem for Leibniz algebras, Bull. Aust. Math. Soc., 86(2) (2012), 184-185.
  • A. Bloh, On a generalization of the concept of Lie algebra, Dokl. Akad. Nauk SSSR, 165 (1965), 471-473.
  • A. Ja. Bloh, A certain generalization of the concept of Lie algebra, Moskov. Gos. Ped. Inst. Ucen. Zap., 375 (1971), 9-20 (in Russian).
  • A. S. Dzhumadil'daev and S. A. Abdykassymova, Leibniz algebras in characteristic p, C. R. Acad. Sci. Paris Ser. I Math., 332(12) (2001), 1047-1052.
  • N. Jacobson, Lie Algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers, New York-London, 1962.
  • M. K. Kinyon and A.Weinstein, Leibniz algebras, Courant algebroids, and multiplications on reductive homogeneous spaces, Amer. J. Math., 123(3) (2001), 525-550.
  • K. Kudaybergenov, M. Ladra and B. Omirov, On Levi-Malcev theorem for Leibniz algebras, Linear Multilinear Algebra, 67(7) (2019), 1471-1482.
  • J.-L. Loday, Cyclic Homology, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 301, Springer- Verlag, Berlin, 1992.
  • J.-L. Loday, Une version non commutative des algebres de Lie: les algebres de Leibniz [A noncommutative version of Lie algebras: the Leibniz algebras], Enseign. Math., 39(2) (1993), 269-293.
  • G. Mason and G. Yamskulna, Leibniz algebras and Lie algebras, SIGMA Symmetry Integrability Geom. Methods Appl., 9 (2013), 063 (10 pp).
  • T. Pirashvili, On Leibniz homology, Ann. Inst. Fourier (Grenoble), 44(2) (1994), 401-411.
  • Z. X. Wan, Lie Algebras, International Series of Monographs in Pure and Applied Mathematics, Vol. 104, Pergamon Press, Oxford-New York-Toronto, Ont., 1975.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Rustam Turdibaev Bu kişi benim

Yayımlanma Tarihi 11 Temmuz 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 26 Sayı: 26

Kaynak Göster

APA Turdibaev, R. (2019). BIPARTITE GRAPHS AND THE STRUCTURE OF FINITE-DIMENSIONAL SEMISIMPLE LEIBNIZ ALGEBRAS. International Electronic Journal of Algebra, 26(26), 122-130. https://doi.org/10.24330/ieja.587009
AMA Turdibaev R. BIPARTITE GRAPHS AND THE STRUCTURE OF FINITE-DIMENSIONAL SEMISIMPLE LEIBNIZ ALGEBRAS. IEJA. Temmuz 2019;26(26):122-130. doi:10.24330/ieja.587009
Chicago Turdibaev, Rustam. “BIPARTITE GRAPHS AND THE STRUCTURE OF FINITE-DIMENSIONAL SEMISIMPLE LEIBNIZ ALGEBRAS”. International Electronic Journal of Algebra 26, sy. 26 (Temmuz 2019): 122-30. https://doi.org/10.24330/ieja.587009.
EndNote Turdibaev R (01 Temmuz 2019) BIPARTITE GRAPHS AND THE STRUCTURE OF FINITE-DIMENSIONAL SEMISIMPLE LEIBNIZ ALGEBRAS. International Electronic Journal of Algebra 26 26 122–130.
IEEE R. Turdibaev, “BIPARTITE GRAPHS AND THE STRUCTURE OF FINITE-DIMENSIONAL SEMISIMPLE LEIBNIZ ALGEBRAS”, IEJA, c. 26, sy. 26, ss. 122–130, 2019, doi: 10.24330/ieja.587009.
ISNAD Turdibaev, Rustam. “BIPARTITE GRAPHS AND THE STRUCTURE OF FINITE-DIMENSIONAL SEMISIMPLE LEIBNIZ ALGEBRAS”. International Electronic Journal of Algebra 26/26 (Temmuz 2019), 122-130. https://doi.org/10.24330/ieja.587009.
JAMA Turdibaev R. BIPARTITE GRAPHS AND THE STRUCTURE OF FINITE-DIMENSIONAL SEMISIMPLE LEIBNIZ ALGEBRAS. IEJA. 2019;26:122–130.
MLA Turdibaev, Rustam. “BIPARTITE GRAPHS AND THE STRUCTURE OF FINITE-DIMENSIONAL SEMISIMPLE LEIBNIZ ALGEBRAS”. International Electronic Journal of Algebra, c. 26, sy. 26, 2019, ss. 122-30, doi:10.24330/ieja.587009.
Vancouver Turdibaev R. BIPARTITE GRAPHS AND THE STRUCTURE OF FINITE-DIMENSIONAL SEMISIMPLE LEIBNIZ ALGEBRAS. IEJA. 2019;26(26):122-30.