Minimal representations of filiform Lie algebras and their application for construction of Leibniz algebras

2019 ◽  
Vol 144 ◽  
pp. 235-244
Author(s):  
I.A. Karimjanov ◽  
M. Ladra
Keyword(s):  
Lie Algebras ◽  
Leibniz Algebras ◽  
Minimal Representations ◽  
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

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

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 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 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.

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

Some new results on Gröbner–Shirshov bases for Lie algebras and around

2018 ◽  
Vol 28 (08) ◽  
pp. 1403-1423
Author(s):  
L. A. Bokut ◽  
Yuqun Chen ◽  
Abdukadir Obul
Keyword(s):  
Lie Algebras ◽  
Associative Algebras ◽  
Leibniz Algebras ◽  
Novikov Algebras

We review Gröbner–Shirshov bases for Lie algebras and survey some new results on Gröbner–Shirshov bases for [Formula: see text]-Lie algebras, Gelfand–Dorfman–Novikov algebras, Leibniz algebras, etc. Some applications are given, in particular, some characterizations of extensions of groups, associative algebras and Lie algebras are given.

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