# Solvable Leibniz algebras with NF n ⊕ [...] F m 1 $\begin{array}{c}{F}_{m}^{1}\end{array}$ nilradical

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

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1371-1388
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topL.M. Camacho, et al. "Solvable Leibniz algebras with NF n ⊕ [...] F m 1 $\begin{array}{} F_{m}^{1} \end{array} $ nilradical." Open Mathematics 15.1 (2017): 1371-1388. <http://eudml.org/doc/288475>.

@article{L2017,

abstract = {All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ [...] Fm1 $\begin\{array\}\{\} F_\{m\}^\{1\} \end\{array\} $ as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and [...] Fm1 $\begin\{array\}\{\} F_\{m\}^\{1\} \end\{array\} $ are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.},

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

journal = {Open Mathematics},

keywords = {Lie algebra; Leibniz algebra; Natural gradation; Null-filiform algebra; Filiform algebra; Solvability; Nilpotence; Nilradical},

language = {eng},

number = {1},

pages = {1371-1388},

title = {Solvable Leibniz algebras with NF n ⊕ [...] F m 1 $\begin\{array\}\{\} F_\{m\}^\{1\} \end\{array\} $ nilradical},

url = {http://eudml.org/doc/288475},

volume = {15},

year = {2017},

}

TY - JOUR

AU - L.M. Camacho

AU - B.A. Omirov

AU - K.K. Masutova

AU - I.M. Rikhsiboev

TI - Solvable Leibniz algebras with NF n ⊕ [...] F m 1 $\begin{array}{} F_{m}^{1} \end{array} $ nilradical

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 1371

EP - 1388

AB - All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ [...] Fm1 $\begin{array}{} F_{m}^{1} \end{array} $ as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and [...] Fm1 $\begin{array}{} F_{m}^{1} \end{array} $ are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.

LA - eng

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

UR - http://eudml.org/doc/288475

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.