Central extensions of null-filiform and naturally graded filiform non-Lie Leibniz algebras

In this paper we describe central extensions of some nilpotent Leibniz algebras. Namely, central extensions of the Leibniz algebra with maximal index of nilpotency are classified. Moreover, non-split central extensions of naturally graded filiform non-Lie Leibniz algebras are described up to isomorp...

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Bibliographic Details
Published in:Journal of algebra 2017-06, Vol.479, p.461-486
Main Authors: Adashev, J.K., Camacho, L.M., Omirov, B.A.
Format: Article
Language:English
Subjects:
2-cocycles
Central extension
Characteristic sequence
Filiform algebra
Leibniz algebra
Natural gradation
Quasi-filiform algebra
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Summary:In this paper we describe central extensions of some nilpotent Leibniz algebras. Namely, central extensions of the Leibniz algebra with maximal index of nilpotency are classified. Moreover, non-split central extensions of naturally graded filiform non-Lie Leibniz algebras are described up to isomorphism. It is shown that k-dimensional central extensions (k≥5) of these algebras are split.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2017.02.003