Solvable Leibniz algebras with naturally graded non-Lie p-filiform nilradicals whose maximal complemented space of its nilradical

J. Q. Adashev; L. M. Camacho; B. A. Omirov

doi:10.1080/03081087.2019.1631742

Solvable Leibniz algebras with naturally graded non-Lie p-filiform nilradicals whose maximal complemented space of its nilradical

J. Q. Adashev
, L. M. Camacho^*
, B. A. Omirov

^*Corresponding author for this work

Academy of Sciences of the Republic of Uzbekistan
University of Seville
National University of Uzbekistan named after Mirzo Ulugbek

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

5 Scopus citations

Abstract

The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded p-filiform non-Lie Leibniz algebra (Formula presented.) and the complemented space to nilradical has maximal dimension, are described up to isomorphism. Moreover, among obtained algebras we indicate the rigid and complete algebras.

Original language	English
Pages (from-to)	1500-1520
Number of pages	21
Journal	Linear and Multilinear Algebra
Volume	69
Issue number	8
DOIs	https://doi.org/10.1080/03081087.2019.1631742
State	Published - 2021
Externally published	Yes

Keywords

Leibniz algebra
derivation
natural gradation
nilradical
p-filiform algebra
solvability
the second group of cohomology

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10.1080/03081087.2019.1631742

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title = "Solvable Leibniz algebras with naturally graded non-Lie p-filiform nilradicals whose maximal complemented space of its nilradical",

abstract = "The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded p-filiform non-Lie Leibniz algebra (Formula presented.) and the complemented space to nilradical has maximal dimension, are described up to isomorphism. Moreover, among obtained algebras we indicate the rigid and complete algebras.",

keywords = "Leibniz algebra, derivation, natural gradation, nilradical, p-filiform algebra, solvability, the second group of cohomology",

author = "Adashev, \{J. Q.\} and Camacho, \{L. M.\} and Omirov, \{B. A.\}",

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year = "2021",

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AU - Adashev, J. Q.

AU - Camacho, L. M.

AU - Omirov, B. A.

PY - 2021

Y1 - 2021

N2 - The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded p-filiform non-Lie Leibniz algebra (Formula presented.) and the complemented space to nilradical has maximal dimension, are described up to isomorphism. Moreover, among obtained algebras we indicate the rigid and complete algebras.

AB - The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded p-filiform non-Lie Leibniz algebra (Formula presented.) and the complemented space to nilradical has maximal dimension, are described up to isomorphism. Moreover, among obtained algebras we indicate the rigid and complete algebras.

KW - Leibniz algebra

KW - derivation

KW - natural gradation

KW - nilradical

KW - p-filiform algebra

KW - solvability

KW - the second group of cohomology

UR - https://www.scopus.com/pages/publications/85067891307

U2 - 10.1080/03081087.2019.1631742

DO - 10.1080/03081087.2019.1631742

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VL - 69

SP - 1500

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JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 8

ER -

Solvable Leibniz algebras with naturally graded non-Lie p-filiform nilradicals whose maximal complemented space of its nilradical

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Keywords

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