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

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

scholarly journals FILIFORM LIE ALGEBRAS OF DIMENSION 8 AS DEGENERATIONS

2014 ◽  
Vol 13 (04) ◽  
pp. 1350144 ◽  
Author(s):  
JOAN FELIPE HERRERA-GRANADA ◽  
PAULO TIRAO
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Nilpotent Lie Algebras ◽  
Filiform Lie Algebras ◽  
Filiform Lie Algebra

For each complex 8-dimensional filiform Lie algebra we find another nonisomorphic Lie algebra that degenerates to it. Since this is already known for nilpotent Lie algebras of rank ≥ 1, only the characteristically nilpotent ones should be considered.

REPRESENTING FILIFORM LIE ALGEBRAS MINIMALLY AND FAITHFULLY BY STRICTLY UPPER-TRIANGULAR MATRICES

2013 ◽  
Vol 12 (04) ◽  
pp. 1250196 ◽  
Author(s):  
MANUEL CEBALLOS ◽  
JUAN NÚÑEZ ◽  
ÁNGEL F. TENORIO
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Nilpotent Lie Algebra ◽  
Algebra Isomorphism ◽  
Triangular Matrices ◽  
Nilpotent Lie Algebras ◽  
Upper Triangular Matrices ◽  
Filiform Lie Algebras ◽  
Filiform Lie Algebra

In this paper, we compute minimal faithful representations of filiform Lie algebras by means of strictly upper-triangular matrices. To obtain such representations, we use nilpotent Lie algebras [Formula: see text]n, of n × n strictly upper-triangular matrices, because any given (filiform) nilpotent Lie algebra [Formula: see text] admits a Lie-algebra isomorphism with a subalgebra of [Formula: see text]n for some n ∈ ℕ\{1}. In this sense, we search for the lowest natural integer n such that the Lie algebra [Formula: see text]n contains the filiform Lie algebra [Formula: see text] as a subalgebra. Additionally, we give a representative of each representation.

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