Representations of nine-dimensional Levi decomposition Lie algebras

2020 ◽  
Vol 224 (3) ◽  
pp. 1340-1363
Author(s):  
Sunil Khanal ◽  
Rishi Raj Subedi ◽  
Gerard Thompson
Keyword(s):  
Lie Algebras ◽  
Levi Decomposition

scholarly journals Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical

2006 ◽  
pp. 309-316 ◽  
Author(s):  
J. M. Ancochea Bermudez ◽  
R. Campoamor – Stursberg ◽  
L. Garcia Vergnolle
Keyword(s):  
Lie Algebras ◽  
Levi Decomposition

scholarly journals Lie Algebras, Structure of Nonlinear Systems and Chaotic Motion

1998 ◽  
Vol 08 (07) ◽  
pp. 1437-1462 ◽  
Author(s):  
S. P. Banks ◽  
D. McCaffrey
Keyword(s):  
Nonlinear Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Approximation Theory ◽  
Chaotic Motion ◽  
Chaotic Systems ◽  
Structure Theory ◽  
New Class ◽  
Levi Decomposition

The structure theory of Lie algebras is used to classify nonlinear systems according to a Levi decomposition and the solvable and semisimple parts of a certain Lie algebra associated with the system. An approximation theory is developed and a new class of chaotic systems is introduced, based on the structure theory of Lie algebras.

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
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