scholarly journals Geometrical/Physical Interpretation of the Conserved Quantities Corresponding to Noether Symmetries of Plane Symmetric Space-Times

2017 ◽  
Vol 2017 ◽  
pp. 1-40 ◽  
Author(s):  
Bismah Jamil ◽  
Tooba Feroze ◽  
Andrés Vargas
Keyword(s):  
Symmetric Space ◽  
Lie Algebras ◽  
Physical Interpretation ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Riemann Curvature ◽  
Plane Symmetric ◽  
Structure Constants ◽  
Curvature Tensors

The aim of this paper is to give the geometrical/physical interpretation of the conserved quantities corresponding to each Noether symmetry of the geodetic Lagrangian of plane symmetric space-times. For this purpose, we present a complete list of plane symmetric nonstatic space-times along with the generators of all Noether symmetries of the geodetic Lagrangian. Additionally, the structure constants of the associated Lie algebras, the Riemann curvature tensors, and the energy-momentum tensors are obtained for each case. It is worth mentioning that the list contains all classes of solutions that have been obtained earlier during the classification of plane symmetric space-times by isometries and homotheties.

A note on classification of teleparallel conformal symmetries in non-static plane symmetric space-times in the teleparallel theory of gravitation using diagonal tetrads

2016 ◽  
Vol 13 (04) ◽  
pp. 1650046 ◽  
Author(s):  
Ghulam Shabbir ◽  
Alamgeer Khan ◽  
M. Amer Qureshi ◽  
A. H. Kara
Keyword(s):  
Symmetric Space ◽  
Vector Fields ◽  
Integration Technique ◽  
Plane Symmetric ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Teleparallel Theory ◽  
Theory Of Gravitation ◽  
Static Plane

In this paper, we explore teleparallel conformal vector fields in non-static plane symmetric space-times in the teleparallel theory of gravitation using the direct integration technique and diagonal tetrads. This study will also cover the static plane symmetric space-times as well. In the teleparallel theory curvature of the non-static plane symmetric space-times is zero and the presence of torsion allows more symmetries. In this study after solving the integrabilty conditions it turns out that the dimension of teleparallel conformal vector fields are 5, 6, 7 or 8.

ON A FERMIONIC REALIZATIONS OF W-TYPE SYMMETRIES

1993 ◽  
Vol 08 (39) ◽  
pp. 3735-3740
Author(s):  
AN. R. KAVALOV ◽  
R.L. MKRTCHYAN
Keyword(s):  
Lie Algebras ◽  
Jordan Algebras ◽  
Free Fermion ◽  
Structure Constants

The simplest W-type algebra is considered, which includes spin-3/2 and 1 currents, with the aim of finding all its realizations in the free fermion theory through the currents of the type γi1…i2sψi1 … ψi2s. The solution of this problem appears to be related to some problem in the theory of Lie algebras, and we give a classification of the solutions for γ tensors, which turn out to be connected with structure constants of Lie algebras. This is in parallel with previously known similar bosonic construction, connected with symmetric counterpart of the Lie algebras — the Jordan algebras.

A Few New 2+1-Dimensional Nonlinear Dynamics and the Representation of Riemann Curvature Tensors

2016 ◽  
Vol 71 (9) ◽  
pp. 777-782
Author(s):  
Yan Wang ◽  
Yufeng Zhang ◽  
Xiangzhi Zhang
Keyword(s):  
Symmetric Space ◽  
Homogeneous Space ◽  
Integrability Condition ◽  
Linear Equations ◽  
Riemann Curvature ◽  
Quadratic Operator ◽  
Stationary Equation ◽  
Linear Evolution ◽  
Linear Evolution Equation ◽  
Curvature Tensors

AbstractWe first introduced a linear stationary equation with a quadratic operator in ∂xand ∂y, then a linear evolution equation is given byN-order polynomials of eigenfunctions. As applications, by takingN=2, we derived a (2+1)-dimensional generalized linear heat equation with two constant parameters associative with a symmetric space. When takingN=3, a pair of generalized Kadomtsev-Petviashvili equations with the same eigenvalues with the case ofN=2 are generated. Similarly, a second-order flow associative with a homogeneous space is derived from the integrability condition of the two linear equations, which is a (2+1)-dimensional hyperbolic equation. WhenN=3, the third second flow associative with the homogeneous space is generated, which is a pair of new generalized Kadomtsev-Petviashvili equations. Finally, as an application of a Hermitian symmetric space, we established a pair of spectral problems to obtain a new (2+1)-dimensional generalized Schrödinger equation, which is expressed by the Riemann curvature tensors.

scholarly journals Classification of real low-dimensional Jacobi (generalized)–Lie bialgebras

2016 ◽  
Vol 14 (01) ◽  
pp. 1750007 ◽  
Author(s):  
A. Rezaei-Aghdam ◽  
M. Sephid
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Three Dimensional ◽  
Lie Bialgebras ◽  
Structure Constants ◽  
Definition Of ◽  
Low Dimensional

We describe the definition of Jacobi (generalized)–Lie bialgebras [Formula: see text] in terms of structure constants of the Lie algebras [Formula: see text] and [Formula: see text] and components of their 1-cocycles [Formula: see text] and [Formula: see text] in the basis of the Lie algebras. Then, using adjoint representations and automorphism Lie groups of Lie algebras, we give a method for classification of real low-dimensional Jacobi–Lie bialgebras. In this way, we obtain and classify real two- and three-dimensional Jacobi–Lie bialgebras.

Classification of Static Spherically Symmetric Spacetimes by Noether Symmetries

2013 ◽  
Vol 52 (10) ◽  
pp. 3534-3542 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
A. G. Johnpillai ◽  
A. H. Kara ◽  
F. M. Mahomed ◽  
F. D. Zaman
Keyword(s):  
Spherically Symmetric ◽  
Noether Symmetries ◽  
Symmetric Spacetimes ◽  
Spherically Symmetric Spacetimes ◽  
Static Spherically Symmetric Spacetimes

scholarly journals Killing and Noether Symmetries of Plane Symmetric Spacetime

2013 ◽  
Vol 52 (9) ◽  
pp. 3106-3117 ◽  
Author(s):  
M. Farasat Shamir ◽  
Adil Jhangeer ◽  
Akhlaq Ahmad Bhatti
Keyword(s):  
Noether Symmetries ◽  
Plane Symmetric ◽  
Symmetric Spacetime
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