scholarly journals Filiform Lie Algebras with Low Derived Length

2020 ◽  
Vol 17 (6) ◽  
Author(s):  
F. J. Castro-Jiménez ◽  
M. Ceballos ◽  
J. Núñez-Valdés
Keyword(s):  
Lie Algebras ◽  
Derived Length ◽  
Filiform Lie Algebras

scholarly journals Links among Characteristically Nilpotent, $C$-Graded and Derived Filiform Lie Algebras

2005 ◽  
Vol 35 (4) ◽  
pp. 1081-1098
Author(s):  
J.C. Benjumea ◽  
F.J. Echarte ◽  
M.C. Márquez ◽  
J. Núñez
Keyword(s):  
Lie Algebras ◽  
Filiform Lie Algebras

Family of p-Filiform Lie Algebras

1998 ◽  
pp. 93-102 ◽  
Author(s):  
J. M. Cabezas ◽  
J. R. Gómez ◽  
A. Jimenez-Merchán
Keyword(s):  
Lie Algebras ◽  
Filiform Lie Algebras

On characteristically nilpotent filiform lie algebras of dimension 9

1995 ◽  
Vol 23 (8) ◽  
pp. 3059-3071 ◽  
Author(s):  
F.J. Castro-Jiménez ◽  
J. Núñez-Valdés
Keyword(s):  
Lie Algebras ◽  
Filiform Lie Algebras

(n– 4)-filiform lie algebras

1999 ◽  
Vol 27 (10) ◽  
pp. 4803-4819 ◽  
Author(s):  
J.M. Cabezas ◽  
J.R. Gómez
Keyword(s):  
Lie Algebras ◽  
Filiform Lie Algebras

scholarly journals Leibniz algebras associated with representations of filiform Lie algebras

2015 ◽  
Vol 98 ◽  
pp. 181-195 ◽  
Author(s):  
Sh.A. Ayupov ◽  
L.M. Camacho ◽  
A.Kh. Khudoyberdiyev ◽  
B.A. Omirov
Keyword(s):  
Lie Algebras ◽  
Leibniz Algebras ◽  
Filiform Lie Algebras

Note on nilpotent and solvable algebras

1955 ◽  
Vol 51 (1) ◽  
pp. 37-40 ◽  
Author(s):  
E. M. Patterson
Keyword(s):  
Lie Algebras ◽  
Linear Algebra ◽  
Derived Length ◽  
Solvable Lie Algebras

In general, the class of a nilpotent linear algebra of dimension n is at most n + 1, and the index, or derived length, of a solvable linear algebra of dimension n is at most n. In this note it is shown that, for a nilpotent linear algebra of dimension n satisfying x2 = 0 for all x, the class is at most n; and bounds are obtained for the indices of solvable Lie algebras.

scholarly journals The cohomology of filiform Lie algebras of maximal rank

2014 ◽  
Vol 455 ◽  
pp. 143-167
Author(s):  
Leandro Cagliero ◽  
Paulo Tirao
Keyword(s):  
Lie Algebras ◽  
Maximal Rank ◽  
Filiform Lie Algebras

ON THE STRUCTURE OF SOLUBLE GRADED LIE ALGEBRAS

2011 ◽  
Vol 10 (04) ◽  
pp. 597-604 ◽  
Author(s):  
PAVEL SHUMYATSKY ◽  
CARMELA SICA
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Graded Lie Algebras ◽  
Derived Length ◽  
Elementary Group ◽  
Graded Lie Algebra

Let A be the elementary group of order 2n and L an A-graded Lie algebra with L0 = 0. Assume that L is soluble with derived length k. It is proved that L has a series of ideals of length n all of whose quotients are nilpotent of {k, n}-bounded class.

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