Solvable Leibniz algebras with NF n ⊕ [...] F m 1 F m 1 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

Abstract

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

How to cite

top

L.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 ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.