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

Year 2019, , 122 - 130, 11.07.2019
https://doi.org/10.24330/ieja.587009

Abstract

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.

References

  • 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.
Year 2019, , 122 - 130, 11.07.2019
https://doi.org/10.24330/ieja.587009

Abstract

References

  • 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.
There are 13 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Rustam Turdibaev This is me

Publication Date July 11, 2019
Published in Issue Year 2019

Cite

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. July 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, no. 26 (July 2019): 122-30. https://doi.org/10.24330/ieja.587009.
EndNote Turdibaev R (July 1, 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, vol. 26, no. 26, pp. 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 (July 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, vol. 26, no. 26, 2019, pp. 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.