Articles

THE CLASSIFICATION OF NILPOTENT LEIBNIZ 3-ALGEBRAS

  • BAI Rui-Pu ,
  • ZHANG Jie
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  • College of Mathematics and Computer Science, Hebei University, Baoding 071002, China

Received date: 2009-09-27

  Online published: 2011-09-20

Supported by

Project partially supported by NSFC (10871192), NSF of Hebei Province (A2010000194).

Abstract

The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.

Cite this article

BAI Rui-Pu , ZHANG Jie . THE CLASSIFICATION OF NILPOTENT LEIBNIZ 3-ALGEBRAS[J]. Acta mathematica scientia, Series B, 2011 , 31(5) : 1997 -2006 . DOI: 10.1016/S0252-9602(11)60377-9

References

[1] Loday J L. Une version non commutative des algebres de Lie: Les algebres de Leibniz. Enseign Math, 1993, 3: 269–293

[2] Ibanez R, Leon M, Marrero J, et al. Leibniz algebroid associated with a Nambu-Poisson structure. J Phys A, 1999, 32: 8129–8144

[3] Kinyon M K, Weinstein A. Leibniz algebras, Courant algebroids, and multiplications on reductive homo-geneous spaces. Amer J Math, 2001, 123: 525–550

[4] Bagger J, Lambert N. Modeling multiple M2’s. Phys Rev D, 2007, 75: 045020

[5] Casas, J M, Loday J L, Pirashvili T. Leibniz n-algebras. Forum Math, 2002, 14: 189–207

[6] Gustavsson A. Algebraic structures on parallel M2-branes. Nucl Phys B, 2009, 811: 66–76

[7] Bagger J, Lambert N. Gauge symmetry and supersymmetry of multiple M2-branes. Phys Rev D, 2008, 77: 065008

[8] Hagiwara Y, Mizutani T. Leibniz algebras associated with foliations. Kodai Math J, 2002, 25: 151–165

[9] Casas J, Insua M, Ladra M. Poincare-Birkhoff-Witt theorem for Leibniz n-algebras. J Symbolic Comput, 2007, 42: 1052–1065

[10] Albeverio S, Ayupov S, Omirov B, et al. Cartan Subalgebras of Leibniz n-Algebras. Comm Alg, 2009, 37(6): 2080–2096

[11] Casas J, Khmaladze E, Ladra M. On Solvability and Nilpotency of Leibniz n-Algebras. Comm Alg, 2006, 34(8): 2769–2780

[12] Bai R, Wang X. Classifications of low dimensional 3-Lie algebras. Acta Math Sci, 2010, 30A(1): 86–96

[13] Bai R, Jia P. The real compact n-Lie algebras and invariant bilinear forms. Acta Math Sci, 2007, 27A(6): 1074–1081

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