Classification of solvable Leibniz algebras with null-filiform nilradical

J. M. Casas; M. Ladra; B. A. Omirov; I. A. Karimjanov

doi:10.1080/03081087.2012.703194

Classification of solvable Leibniz algebras with null-filiform nilradical

J. M. Casas
, M. Ladra
, B. A. Omirov
, I. A. Karimjanov

University of Vigo
University of Santiago de Compostela
Institute of Mathematics and Information Technologies of Academy of Uzbekistan

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

61 Scopus citations

Abstract

In this article we classify solvable Leibniz algebras whose nilradical is a null-filiform algebra. We extend the obtained classification to the case when the solvable Leibniz algebra is decomposed as a direct sum of its nilradical, which is a direct sum of null-filiform ideals and a one-dimensional complementary subspace. Moreover, in this case we establish that these ideals are ideals of the algebra as well.

Original language	English
Pages (from-to)	758-774
Number of pages	17
Journal	Linear and Multilinear Algebra
Volume	61
Issue number	6
DOIs	https://doi.org/10.1080/03081087.2012.703194
State	Published - Jun 2013
Externally published	Yes

Keywords

Leibniz algebra
nilpotence
nilradical
null-filiform algebra
solvability

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10.1080/03081087.2012.703194

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abstract = "In this article we classify solvable Leibniz algebras whose nilradical is a null-filiform algebra. We extend the obtained classification to the case when the solvable Leibniz algebra is decomposed as a direct sum of its nilradical, which is a direct sum of null-filiform ideals and a one-dimensional complementary subspace. Moreover, in this case we establish that these ideals are ideals of the algebra as well.",

keywords = "Leibniz algebra, nilpotence, nilradical, null-filiform algebra, solvability",

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N2 - In this article we classify solvable Leibniz algebras whose nilradical is a null-filiform algebra. We extend the obtained classification to the case when the solvable Leibniz algebra is decomposed as a direct sum of its nilradical, which is a direct sum of null-filiform ideals and a one-dimensional complementary subspace. Moreover, in this case we establish that these ideals are ideals of the algebra as well.

AB - In this article we classify solvable Leibniz algebras whose nilradical is a null-filiform algebra. We extend the obtained classification to the case when the solvable Leibniz algebra is decomposed as a direct sum of its nilradical, which is a direct sum of null-filiform ideals and a one-dimensional complementary subspace. Moreover, in this case we establish that these ideals are ideals of the algebra as well.

KW - Leibniz algebra

KW - nilpotence

KW - nilradical

KW - null-filiform algebra

KW - solvability

UR - https://www.scopus.com/pages/publications/84875473287

U2 - 10.1080/03081087.2012.703194

DO - 10.1080/03081087.2012.703194

M3 - 文章

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EP - 774

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 6

ER -

Classification of solvable Leibniz algebras with null-filiform nilradical

Abstract

Keywords

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