The realization and structure of complete Lie algebras whose nilpotent radicals are Heisenberg algebras

1998 ◽  
Vol 43 (5) ◽  
pp. 383-385 ◽  
Author(s):  
Cuibo Jiang ◽  
Daoji Meng
Keyword(s):  
Lie Algebras ◽  
Heisenberg Algebras

Complete lie algebras and heisenberg algebras*

1994 ◽  
Vol 22 (13) ◽  
pp. 5509-5524 ◽  
Author(s):  
Dao Ji Meng
Keyword(s):  
Lie Algebras ◽  
Heisenberg Algebras

DERIVATION ALGEBRAS OF RINGS RELATED TO HEISENBERG ALGEBRAS

2004 ◽  
Vol 03 (02) ◽  
pp. 181-191 ◽  
Author(s):  
JEFFREY BERGEN
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Quotient Ring ◽  
Finite Codimension ◽  
Enveloping Algebras ◽  
Cartan Type ◽  
Direct Sum ◽  
Heisenberg Algebras ◽  
Martindale Quotient Ring ◽  
The Ideal

In this paper, we will determine the Lie algebra of derivations of rings which are generalizations of the enveloping algebras of Heisenberg Lie algebras. First, we will determine which derivations are X-inner and also determine which elements in the Martindale quotient ring induce X-inner derivations. Then, we will show that the Lie algebra of derivations is the direct sum of the ideal of X-inner derivations and a subalgebra which is isomorphic to a subalgebra of finite codimension in a Cartan type Lie algebra.

Generalized Heisenberg Algebras and Toroidal Lie Algebras

2010 ◽  
Vol 17 (03) ◽  
pp. 375-388 ◽  
Author(s):  
Yingjue Fang ◽  
Liangang Peng
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Heisenberg Algebra ◽  
Simple Lie Algebras ◽  
Simple Lie Algebra ◽  
Heisenberg Algebras ◽  
Toroidal Lie Algebra

In this article we provide two kinds of infinite presentations of toroidal Lie algebras. At first we define generalized Heisenberg algebras and prove that each toroidal Lie algebra is an amalgamation of a simple Lie algebra and a generalized Heisenberg algebra in the sense of Saito and Yoshii. This is one kind of presentations of toroidal Lie algebras given by the generators of generalized Heisenberg algebras and the Chevalley generators of simple Lie algebras with certain amalgamation relations. Secondly by using the generalized Chevalley generators, we give another kind of presentations. These two kinds of presentations are different from those given by Moody, Eswara Rao and Yokonuma.

BEYOND UNITARY PARASUPERSYMMETRY FROM THE VIEWPOINT OF h3 AND h4 HEISENBERG ALGEBRAS

2006 ◽  
Vol 21 (30) ◽  
pp. 2303-2312 ◽  
Author(s):  
A. CHENAGHLOU ◽  
H. FAKHRI
Keyword(s):  
Harmonic Oscillator ◽  
Lie Algebras ◽  
Flat Surface ◽  
Arbitrary Order ◽  
Hamiltonian Operator ◽  
Mean Value ◽  
Heisenberg Algebras ◽  
Unitary Condition ◽  
The Mean ◽  
Special Case

Using the partition of the number p-1 into p-1 real parts which are not equal with each other necessarily, we develop the unitary parasupersymmetry algebra of arbitrary order p so that the well-known Rubakov–Spiridonov–Khare parasupersymmetry becomes a special case of the developed one. It is shown that the developed algebra is realized by simple harmonic oscillator and Landau problem on a flat surface with the symmetries of h3 and h4 Heisenberg–Lie algebras. For this new parasupersymmetry, the well-known unitary condition is violated, however, unitarity of the corresponding algebra is structurally conserved. Moreover, the components of the bosonic Hamiltonian operator are derived as functions from the mean value of the partition numbers with their label weight function.

scholarly journals Characterization of Simple Highest Weight Modules

2013 ◽  
Vol 56 (3) ◽  
pp. 606-614 ◽  
Author(s):  
Volodymyr Mazorchuk ◽  
Kaiming Zhao
Keyword(s):  
Lie Algebras ◽  
Positive Root ◽  
Virasoro Algebra ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Heisenberg Algebras ◽  
Higher Rank ◽  
Highest Weight Modules ◽  
Weight Modules

Abstract.We prove that for simple complex finite dimensional Lie algebras, affine Kac–Moody Lie algebras, the Virasoro algebra, and the Heisenberg–Virasoro algebra, simple highest weight modules are characterized by the property that all positive root elements act on these modules locally nilpotently. We also show that this is not the case for higher rank Virasoro algebras and for Heisenberg 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.

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