scholarly journals ON LIE-LIKE COMPLEX FILIFORM LEIBNIZ ALGEBRAS

2009 ◽  
Vol 79 (3) ◽  
pp. 391-404 ◽  
Author(s):  
B. A. OMIROV ◽  
I. S. RAKHIMOV
Keyword(s):  
Computer Program ◽  
Lie Algebras ◽  
Effective Algorithm ◽  
Leibniz Algebras ◽  
Fixed Dimension ◽  
Structure Constants ◽  
Filiform Lie Algebras

AbstractIn this paper we propose an approach to classifying a subclass of filiform Leibniz algebras. This subclass arises from the naturally graded filiform Lie algebras. We reconcile and simplify the structure constants of such a class. In the arbitrary fixed dimension case an effective algorithm to control the behavior of the structure constants under adapted transformations of basis is presented. In one particular case, the precise formulas for less than 10 dimensions are given. We provide a computer program in Maple that can be used in computations as well.

On isomorphism criterion for a subclass of complex filiform Leibniz algebras

2017 ◽  
Vol 27 (07) ◽  
pp. 953-972
Author(s):  
I. S. Rakhimov ◽  
A. Kh. Khudoyberdiyev ◽  
B. A. Omirov ◽  
K. A. Mohd Atan
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Central Extension ◽  
Linear Deformation ◽  
Leibniz Algebras ◽  
Structure Constants ◽  
Filiform Lie Algebras ◽  
Filiform Lie Algebra ◽  
Isomorphism Criterion

In this paper, we present an algorithm to give the isomorphism criterion for a subclass of complex filiform Leibniz algebras arising from naturally graded filiform Lie algebras. This subclass appeared as a Leibniz central extension of a linear deformation of filiform Lie algebra. We give the table of multiplication choosing appropriate adapted basis, identify the elementary base changes and describe the behavior of structure constants under these base changes, then combining them the isomorphism criterion is given. The final result of calculations for one particular case also is provided.

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

Solvable Leibniz algebras with quasi-filiform Lie algebras of maximum length nilradicals

2020 ◽  
Vol 48 (8) ◽  
pp. 3525-3542
Author(s):  
Kh. A. Muratova ◽  
M. Ladra ◽  
B. A. Omirov ◽  
A. M. Sattarov
Keyword(s):  
Lie Algebras ◽  
Maximum Length ◽  
Leibniz Algebras ◽  
Filiform Lie Algebras

scholarly journals Almost Inner Derivations of Some Nilpotent Leibniz Algebras

2020 ◽  
pp. 733-745
Author(s):  
Zhobir K. Adashev ◽  
Tuuelbay K. Kurbanbaev
Keyword(s):  
Lie Algebras ◽  
Leibniz Algebras ◽  
Finite Dimensional ◽  
Filiform Lie Algebras

We investigate almost inner derivations of some finite-dimensional nilpotent Leibniz algebras. We show the existence of almost inner derivations of Leibniz filiform non-Lie algebras differing from inner derivations, we also show that the almost inner derivations of some filiform Leibniz algebras containing filiform Lie algebras do not coincide with inner derivations

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

scholarly journals Pseudo-metric 2-step nilpotent Lie algebras

2018 ◽  
Vol 18 (2) ◽  
pp. 237-263 ◽  
Author(s):  
Christian Autenried ◽  
Kenro Furutani ◽  
Irina Markina ◽  
Alexander Vasiľev
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Nilpotent Lie Algebra ◽  
Rational Structure ◽  
Lie Triple System ◽  
Nilpotent Lie Algebras ◽  
Lie Bracket ◽  
Orthogonal Lie Algebra ◽  
Structure Constants ◽  
Scalar Products

Abstract The metric approach to studying 2-step nilpotent Lie algebras by making use of non-degenerate scalar products is realised. We show that a 2-step nilpotent Lie algebra is isomorphic to its standard pseudo-metric form, that is a 2-step nilpotent Lie algebra endowed with some standard non-degenerate scalar product compatible with the Lie bracket. This choice of the standard pseudo-metric form allows us to study the isomorphism properties. If the elements of the centre of the standard pseudo-metric form constitute a Lie triple system of the pseudo-orthogonal Lie algebra, then the original 2-step nilpotent Lie algebra admits integer structure constants. Among particular applications we prove that pseudo H-type algebras have bases with rational structure constants, which implies that the corresponding pseudo H-type groups admit lattices.

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
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