相关论文: Group analysis of structure equations for stars in…
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on…
Different group structures which underline the integrable systems are considered. In some cases, the quantization of the integrable system can be provided with substituting groups by their quantum counterparts. However, some other group…
This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…
We have found some new exact static spherically symmetric interior solutions of metric $f(R)$ gravitational theories describing the equilibrium configuration of a star. Then the solution is matched to the exterior solution and thus gives a…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
This paper presents algebraic methods for the study of polynomial relative invariants, when the group G formed by the symmetries and relative symmetries is a compact Lie group. We deal with the case when the subgroup H of symmetries is…
The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…
Full set of autonomous completely solvable differential systems of equations in total differentials is built by basis of infinitesimal operators, universal invariant, and structure constants of admited multiparametric Lie group (abelian and…
The determination of the properties of neutron stars from the underlying theory, QCD, is still an unsolved problem. This is mainly due to the difficulty to obtain reliable results for the equation of state for cold, dense QCD. As an…
A new class of solutions describing analytical solutions for compact stellar structures has been developed within the tenets of General Relativity. Considering the inherent anisotropy in compact stars, a stable and causal model for…
We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus,…
Let $\mathcal{C}$ be a conjugacy class of involutions in a group $G$. We study the graph $\Gamma(\mathcal{C})$ whose vertices are elements of $\mathcal{C}$ with $g,h\in\mathcal{C}$ connected by an edge if and only if $gh\in\mathcal{C}$. For…
We use group homology to define invariants in algebraic K-theory and in an analogue of the Bloch group for Q-rank one lattices and for some other geometric structures. We also show that the Bloch invariants of CR structures and of flag…
We present the relativistic hydrostatic equilibrium equations for a wide class of gravitational theories possessing a scalar-tensor representation. It turns out that the stellar structure equations can be written with respect to the…
Lie symmetry group method is applied to study the Telegraph equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…
Spectra of late-type stars are usually analyzed with static model atmospheres in local thermodynamic equilibrium (LTE) and a homogeneous plane-parallel or spherically symmetric geometry. The energy balance requires particular attention, as…
We study a nonlinear system of partial differential equations which describe rotating shallow water with an arbitrary constant polytropic index $\gamma $ for the fluid. In our analysis we apply the theory of symmetries for differential…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
Crystals which have a uniform distribution of defects are endowed with a Lie group description which allows one to construct an associated discrete structure. These structures are in fact the discrete subgroups of the ambient Lie group. The…