Soluble lie algebras with one defining relation

1982 ◽  
Vol 22 (4) ◽  
pp. 620-625 ◽  
Author(s):  
V. V. Talapov
Keyword(s):  
Lie Algebras ◽  
Defining Relation

ON ISOMORPHISM OF LIE ALGEBRAS WITH ONE DEFINING RELATION

2004 ◽  
Vol 14 (03) ◽  
pp. 389-393 ◽  
Author(s):  
ALEXANDER A. MIKHALEV ◽  
VLADIMIR SHPILRAIN ◽  
UALBAI U. UMIRBAEV
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Free Lie Algebra ◽  
Finitely Generated ◽  
Defining Relation

Let L be a finitely generated free Lie algebra. We construct an example of two elements u and v of L such that the factor algebras L/(u) and L/(v) are isomorphic, where (u) and (v) are ideals of L generated by u and v, respectively, but there is no automorphism φ of L such that φ(u)=v.

The rigidity of some solvable Lie algebras

2018 ◽  
Vol 2018 (2) ◽  
pp. 43-49
Author(s):  
R.K. Gaybullaev ◽  
Kh.A. Khalkulova ◽  
J.Q. Adashev
Keyword(s):  
Lie Algebras ◽  
Solvable Lie Algebras

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

2018 ◽  
Vol 13 (3) ◽  
pp. 59-63 ◽  
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Gas Dynamics ◽  
Hydrodynamic Type ◽  
System Of Equations ◽  
Two Dimensional ◽  
Equations Of Gas Dynamics ◽  
Entropy Functions

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

scholarly journals Abelian extensions and crossed modules of Hom-Lie algebras

2020 ◽  
Vol 224 (3) ◽  
pp. 987-1008
Author(s):  
José Manuel Casas ◽  
Xabier García-Martínez
Keyword(s):  
Lie Algebras ◽  
Abelian Extensions ◽  
Crossed Modules

On parakähler Hom-Lie algebras and Hom-left-symmetric bialgebras

2016 ◽  
Vol 45 (1) ◽  
pp. 105-120 ◽  
Author(s):  
Qinxiu Sun ◽  
Hongliang Li
Keyword(s):  
Lie Algebras

Lie algebras graded by the weight system (Θ ,sl)

2021 ◽  
Vol 581 ◽  
pp. 1-44
Author(s):  
Alexander Baranov ◽  
Hogir M. Yaseen
Keyword(s):  
Lie Algebras ◽  
Weight System
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