Ricci inheritance collineations in Bianchi type II spacetime

2016 ◽  
Vol 31 (17) ◽  
pp. 1650102 ◽  
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar ◽  
Ashfaque H. Bokhari ◽  
Suhail Khan
Keyword(s):  
Lie Algebra ◽  
Ricci Tensor ◽  
Bianchi Type ◽  
Complete Classification ◽  
Type Ii

In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6.

λ-Mappings Between Representation Rings of Lie Algebras

1983 ◽  
Vol 35 (5) ◽  
pp. 898-960 ◽  
Author(s):  
R. V. Moody ◽  
A. Pianzola
Keyword(s):  
Root System ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Cartan Subalgebra ◽  
Complete Classification ◽  
Representation Rings ◽  
Mathematical Formalization ◽  
Intuitive Idea ◽  
Image Position

In [10] Patera and Sharp conceived a new relation, subjoining, between semisimple Lie algebras. Our objective in this paper is twofold. Firstly, to lay down a mathematical formalization of this concept for arbitrary Lie algebras. Secondly, to give a complete classification of all maximal subjoinings between Lie algebras of the same rank, of which many examples were already known to the above authors.The notion of subjoining is a generalization of the subalgebra relation between Lie algebras. To give an intuitive idea of what is involved we take a simple example. Suppose is a complex simple Lie algebra of type B2. Let be a Cartan subalgebra of and Δ the corresponding root system. We have the standard root diagramInside B2 there lies the subalgebra A1 × A1 which can be identified with the sum of and the root spaces corresponding to the long roots of B2.

scholarly journals Lie symmetries and singularity analysis for generalized shallow-water equations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 739-747
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Lie Algebra ◽  
Three Dimensional ◽  
Singularity Analysis ◽  
Complete Classification ◽  
Similarity Solutions ◽  
Lie Symmetries ◽  
Reduced Equations ◽  
Complete Study ◽  
The One

AbstractWe perform a complete study by using the theory of invariant point transformations and the singularity analysis for the generalized Camassa-Holm (CH) equation and the generalized Benjamin-Bono-Mahoney (BBM) equation. From the Lie theory we find that the two equations are invariant under the same three-dimensional Lie algebra which is the same Lie algebra admitted by the CH equation. We determine the one-dimensional optimal system for the admitted Lie symmetries and we perform a complete classification of the similarity solutions for the two equations of our study. The reduced equations are studied by using the point symmetries or the singularity analysis. Finally, the singularity analysis is directly applied on the partial differential equations from where we infer that the generalized equations of our study pass the singularity test and are integrable.

scholarly journals 2-Local derivations on the W-algebra W(2,2)

2020 ◽  
pp. 2150237
Author(s):  
Xiaomin Tang
Keyword(s):  
Lie Algebra ◽  
Complete Classification ◽  
Infinite Dimensional ◽  
Local Derivation ◽  
Infinite Dimensional Lie Algebra

This paper is devoted to study 2-local derivations on [Formula: see text]-algebra [Formula: see text] which is an infinite-dimensional Lie algebra with some outer derivations. We prove that all 2-local derivations on the [Formula: see text]-algebra [Formula: see text] are derivations. We also give a complete classification of the 2-local derivation on the so-called thin Lie algebra and prove that it admits many 2-local derivations which are not derivations.

scholarly journals Maximally inflected real trigonal curves on Hirzebruch surfaces

2021 ◽  
pp. 331-345
Author(s):  
V. Zvonilov
Keyword(s):  
Complete Classification ◽  
Type I ◽  
Type Ii ◽  
Simple Graphs ◽  
Content Type ◽  
Hirzebruch Surfaces ◽  
Trigonal Curves ◽  
Arbitrary Genus

In 2014 A. Degtyarev, I. Itenberg, and the author gave a description, up to fiberwise equivariant deformations, of maximally inflected real trigonal curves of type I (over a base B B of an arbitrary genus) in terms of the combinatorics of sufficiently simple graphs and for B = P 1 B=\mathbb {P}^1 obtained a complete classification of such curves. In this paper, the mentioned results are extended to maximally inflected real trigonal curves of type II over B = P 1 B=\mathbb {P}^1 .

scholarly journals AN ECOSYSTEM WITH HTII RESPONSE AND PREDATORS’ GENETIC VARIABILITY

2014 ◽  
Vol 19 (3) ◽  
pp. 371-394 ◽  
Author(s):  
Clara Viberti ◽  
Ezio Venturino
Keyword(s):  
Genetic Variability ◽  
Response Function ◽  
Environmental Effects ◽  
Numerical Experiments ◽  
Complete Classification ◽  
Stability Conditions ◽  
Type Ii ◽  
Hurwitz Stability ◽  
Function Modelling

A new model to investigate environmental effects of genetically distinguishable predators is presented. The Holling type II response function, modelling feeding satiation, leads to persistent system's oscillations, as in classical population models. An almost complete classification of the cases arising in the Routh–Hurwitz stability conditions mathematically characterizes the paper. It is instrumental as a guideline in the numerical experiments leading to the findings on the limit cycles. This result extends what found in an earlier parallel investigation containing a standard bilinear response function.

scholarly journals Classification of Kantowski–Sachs metric via conformal Ricci collineations

2017 ◽  
Vol 15 (01) ◽  
pp. 1850006 ◽  
Author(s):  
Tahir Hussain ◽  
Fawad Khan ◽  
Ashfaque H. Bokhari ◽  
Sumaira Saleem Akhtar
Keyword(s):  
Lie Algebra ◽  
Physical Interpretation ◽  
Ricci Tensor ◽  
Ricci Collineations ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Spacetime Metric

In this paper, we present a classification of the Kantowski–Sachs spacetime metric according to its conformal Ricci collineations (CRCs). Solving the CRC equations, it is shown that the Kantowski–Sachs metric admits 15-dimensional Lie algebra of CRCs when its Ricci tensor is non-degenerate and an infinite dimensional group of CRCs when the Ricci tensor is degenerate. Some examples of Kantowski–Sachs metric admitting nontrivial CRCs are presented and their physical interpretation is provided.

scholarly journals Sistema óptimo, soluciones invariantes y clasificación completa del grupo de simetrías de Lie para la ecuación de Kummer-Schwarz generalizada y su representación del álgebra de Lie

2021 ◽  
Vol 39 (2) ◽  
Author(s):  
Danilo García Hernández ◽  
Oscar Mario Londoño Duque ◽  
Yeisson Acevedo ◽  
Gabriel Loaiza
Keyword(s):  
Symmetry Group ◽  
Lie Algebra ◽  
Complete Classification ◽  
Lie Symmetry ◽  
Invariant Solutions ◽  
Generating Operators ◽  
Alternative Solutions ◽  
Schwarz Equation

We obtain the complete classification of the Lie symmetry group and the optimal system’s generating operators associated with a particular case of the generalized Kummer - Schwarz equation. Using those operators we characterize all invariant solutions, alternative solutions were found for the equation studied and the Lie algebra associated with the symmetry group is classified.

scholarly journals Classification theorem on irreducible representations of theq-deformed algebraU′q(son)

2005 ◽  
Vol 2005 (2) ◽  
pp. 225-262 ◽  
Author(s):  
N. Z. Iorgov ◽  
A. U. Klimyk
Keyword(s):  
Lie Algebra ◽  
Complete Classification ◽  
Universal Enveloping Algebra ◽  
Irreducible Representations ◽  
Classical Type ◽  
Enveloping Algebra ◽  
Root Of Unity ◽  
Complete Reducibility ◽  
Finite Dimensional

The aim of this paper is to give a complete classification of irreducible finite-dimensional representations of the nonstandardq-deformationU′q(son)(which does not coincide with the Drinfel'd-Jimbo quantum algebraUq(son)) of the universal enveloping algebraU(son(ℂ))of the Lie algebrason(ℂ)whenqis not a root of unity. These representations are exhausted by irreducible representations of the classical type and of the nonclassical type. The theorem on complete reducibility of finite-dimensional representations ofU′q(son)is proved.

scholarly journals Post-Lie Algebra Structures on the Lie Algebragl(2,C)

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yuqiu Sheng ◽  
Xiaomin Tang
Keyword(s):  
Lie Algebra ◽  
Complete Classification

The post-Lie algebra is an enriched structure of the Lie algebra. We give a complete classification of post-Lie algebra structures on the Lie algebragl(2,C)up to isomorphism.

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