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On a Description of Irreducible Component in the Set of Nilpotent Leibniz Algebras Containing the Algebra of Maximal Nilindex, and Classification of Graded Filiform Leibniz Algebras

In: Computer Algebra in Scientific Computing

Author

Listed:
  • Sh. A. Ayupov

    (Samarkand State University)

  • B. A. Omirov

    (Samarkand State University)

Abstract

This paper is devoted to the study of Leibniz algebras introduced by Loday in [1-2] as an analogue of zero ”noncommutative” Lie algebras. We define the notion of zero-filiform Leibniz algebras and study their properties. There is a notion of p-filiform Lie algebras for p≥ 1 [3], which loses a sense in case p = 0, since Lie algebra has at least two generators. In the case of Leibniz algebras for p = 0 this notion substantial, and thereby, introduction of a zero-filiform algebra is quite natural. We also investigate the complex non-Lie filiform Leibniz algebras. In particular, we give some equivalent conditions of filiformity of Leibniz algebras and describe complex Leibniz algebras, which were graded in natural way.

Suggested Citation

  • Sh. A. Ayupov & B. A. Omirov, 2000. "On a Description of Irreducible Component in the Set of Nilpotent Leibniz Algebras Containing the Algebra of Maximal Nilindex, and Classification of Graded Filiform Leibniz Algebras," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing, pages 21-34, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-57201-2_3
    DOI: 10.1007/978-3-642-57201-2_3
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