On Classification of Filiform Leibniz Algebras

J. R. Gómez; B. A. Omirov

doi:10.1142/S1005386715000668

On Classification of Filiform Leibniz Algebras

J. R. Gómez
, B. A. Omirov^*

^*Corresponding author for this work

University of Seville
National University of Uzbekistan named after Mirzo Ulugbek

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

In this work we prove that in classifying of filiform Leibniz algebras whose naturally graded algebra is a non-Lie algebra, it suffices to consider some special basis transformations. Moreover, we derive a criterion for two such Leibniz algebras to be isomorphic in terms of such transformations. The classification problem of filiform Leibniz algebras whose naturally graded algebra is non-Lie in an arbitrary dimension, is reduced to the investigation of the conditions obtained.

Original language	English
Pages (from-to)	757-774
Number of pages	18
Journal	Algebra Colloquium
Volume	22
DOIs	https://doi.org/10.1142/S1005386715000668
State	Published - 1 Dec 2015
Externally published	Yes

Keywords

Leibniz algebra
Lie algebra
adapted basis
filiform Leibniz algebra
natural gradation

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10.1142/S1005386715000668

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abstract = "In this work we prove that in classifying of filiform Leibniz algebras whose naturally graded algebra is a non-Lie algebra, it suffices to consider some special basis transformations. Moreover, we derive a criterion for two such Leibniz algebras to be isomorphic in terms of such transformations. The classification problem of filiform Leibniz algebras whose naturally graded algebra is non-Lie in an arbitrary dimension, is reduced to the investigation of the conditions obtained.",

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N2 - In this work we prove that in classifying of filiform Leibniz algebras whose naturally graded algebra is a non-Lie algebra, it suffices to consider some special basis transformations. Moreover, we derive a criterion for two such Leibniz algebras to be isomorphic in terms of such transformations. The classification problem of filiform Leibniz algebras whose naturally graded algebra is non-Lie in an arbitrary dimension, is reduced to the investigation of the conditions obtained.

AB - In this work we prove that in classifying of filiform Leibniz algebras whose naturally graded algebra is a non-Lie algebra, it suffices to consider some special basis transformations. Moreover, we derive a criterion for two such Leibniz algebras to be isomorphic in terms of such transformations. The classification problem of filiform Leibniz algebras whose naturally graded algebra is non-Lie in an arbitrary dimension, is reduced to the investigation of the conditions obtained.

KW - Leibniz algebra

KW - Lie algebra

KW - adapted basis

KW - filiform Leibniz algebra

KW - natural gradation

UR - https://www.scopus.com/pages/publications/84946722650

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ER -

On Classification of Filiform Leibniz Algebras

Abstract

Keywords

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