We perform a systematic study of the recently discovered fundamental plane galaxy clusters (CFP) using ~250 simulated from The Three Hundred project, focusing on stability against different temperature definitions and its dependence dynamical relaxation state clusters. CFP is characterised by $T\propto M_\mathrm{s}^\alpha\,r_\mathrm{s}^\beta$, defined with gas ($T$) characteristic halo scale ra...

Considering prolongation of a Lie algebroid equipped with a spray, defining some classical tensors, we show that a Lie symmetry of a spray is a curvature collineation for these tensors.

in this article, we introduce monomial irreducible representations of the special linear lie algebra $sln$. we will show that this kind of representations have bases for which the action of the chevalley generators of the lie algebra on the basis elements can be given by a simple formula.

‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry ...

Some Lie algebra analogues of Schur's theorem and its converses are presented. As a result, it is shown that for a capable Lie algebra L we always have dim L=Z(L) 2(dim(L2))2. We also give give some examples sup- porting our results.

In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.

‎In this paper Lie symmetry analysis is applied in order to find new solutions for Fokker Plank equation of Ornstein-Uhlenbeck process‎. ‎This analysis classifies the solutions format of the Fokker Plank equation by using the Lie algebra of the symmetries of our considered stochastic process‎.

We extend the construction of the authors’ paper of 2002 by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby obtain a universal algebra of generalized tensor fields canonically containing the space of distributional tensor fields. The canonical...

A possible notion of superspace associated to a given 3-dimensional Lie algebra g0 might be a Lie superalgebra g g0 ⊕ g1. If one is to introduce a minimal set of assumptions, it seems quite natural to consider those superalgebras for which g1 g0 and for which the g0 action on g1 is the adjoint representation. A complete classification of the real and complex 3, 3 -dimensional Lie superalgebras ...

Let g be a reductive Lie algebra over C. We say that a g-module M is a generalized Harish-Chandra module if, for some subalgebra k ⊂ g, M is locally k-finite and has finite k-multiplicities. We believe that the problem of classifying all irreducible generalized Harish-Chandra modules could be tractable. In this paper, we review the recent success with the case when k is a Cartan subalgebra. We ...