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

Yıl 2019, , 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, , 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

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.