Solvable Leibniz algebras with NFn F1m nilradical

L. M. Camacho; B. A. Omirov; K. K. Masutova; I. M. Rikhsiboev

doi:10.1515/math-2017-0115

Solvable Leibniz algebras with NF_n F¹_m nilradical

L. M. Camacho
, B. A. Omirov
, K. K. Masutova
, I. M. Rikhsiboev^*

^*Corresponding author for this work

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

1 Scopus citations

Abstract

All finite-dimensional solvable Leibniz algebras L, having N = NF_n F_m¹ F_m¹ as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NF_n and F_m¹ F_m¹ are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.

Original language	English
Pages (from-to)	1371-1388
Number of pages	18
Journal	Open Mathematics
Volume	15
Issue number	1
DOIs	https://doi.org/10.1515/math-2017-0115
State	Published - 2017
Externally published	Yes

Keywords

Filiform algebra
Leibniz algebra
Lie algebra
Natural gradation
Nilpotence
Nilradical
Null-filiform algebra
Solvability

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10.1515/math-2017-0115

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title = "Solvable Leibniz algebras with NFn F1m nilradical",

abstract = "All finite-dimensional solvable Leibniz algebras L, having N = NFn Fm1 Fm1 as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and Fm1 Fm1 are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.",

keywords = "Filiform algebra, Leibniz algebra, Lie algebra, Natural gradation, Nilpotence, Nilradical, Null-filiform algebra, Solvability",

author = "Camacho, \{L. M.\} and Omirov, \{B. A.\} and Masutova, \{K. K.\} and Rikhsiboev, \{I. M.\}",

note = "Publisher Copyright: {\textcopyright} 2017 Camacho et al.",

year = "2017",

doi = "10.1515/math-2017-0115",

language = "英语",

volume = "15",

pages = "1371--1388",

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T1 - Solvable Leibniz algebras with NFn F1m nilradical

AU - Camacho, L. M.

AU - Omirov, B. A.

AU - Masutova, K. K.

AU - Rikhsiboev, I. M.

PY - 2017

Y1 - 2017

N2 - All finite-dimensional solvable Leibniz algebras L, having N = NFn Fm1 Fm1 as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and Fm1 Fm1 are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.

AB - All finite-dimensional solvable Leibniz algebras L, having N = NFn Fm1 Fm1 as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and Fm1 Fm1 are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.

KW - Filiform algebra

KW - Leibniz algebra

KW - Lie algebra

KW - Natural gradation

KW - Nilpotence

KW - Nilradical

KW - Null-filiform algebra

KW - Solvability

UR - https://www.scopus.com/pages/publications/85040335719

U2 - 10.1515/math-2017-0115

DO - 10.1515/math-2017-0115

M3 - 文章

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SN - 1895-1074

VL - 15

SP - 1371

EP - 1388

JO - Open Mathematics

JF - Open Mathematics

IS - 1

ER -

Solvable Leibniz algebras with NF_n F¹_m nilradical

Abstract

Keywords

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