Related papers: Linear Representation of Lie Group
For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…
A difference Lie group is a Lie group equipped with a difference operator, equivalently a crossed homomorphism with respect to the adjoint action. In this paper, first we introduce the notion of a representation of a difference Lie group,…
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
In this paper, we study invariants of linear differential operators with respect to algebraic Lie pseudogroups. Then we use these invariants and the principle of n-invariants to get normal forms (or models) of the differential operators and…
This book encompasses both traditional and modern methods treating partial differential equation (PDE) of first order and second order. There is a balance in making a selfcontained mathematical text and introducing new subjects. The Lie…
We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which…
In this survey we discuss a wide variety of aspects related to Lie group integrators. These numerical integration schemes for differential equations on manifolds have been studied in a general and systematic manner since the 1990s and the…
Given a representation V of a group G, there are two natural ways of defining a representation of the group algebra k[G] in the external power V^{\wedge m}. The set L(V) of elements of k[G] for which these two ways give the same result is a…
In this paper we perform Lie group analysis of systems of partial differential equations which describe different cases of classical plasma equilibria, and find groups of transformations admitted by those equations in several important…
Harmonic functions of the three dimensional Lie groups defined on certain manifolds related to the Lie groups themselves and carrying all their unitary representations are explicitly constructed. The realisations of these Lie groups are…
The aim of this paper is to present aspects of the use of Lie groups in mechanics. We start with the motion of the rigid body for which the main concepts are extracted. In a second part, we extend the theory for an arbitrary Lie group and…
This is an overview article on compact Lie groups and their representations, written for the Encyclopedia of Mathematical Physics to be published by Elsevier.
There has been some work in the literature on limit theorems for the trace of commutators for compact Lie groups. We revisit this from the perspective of combinatorial representation theory.
In this note we survey results in recent research papers on the use of Lie groups in the study of partial differential equations. The focus will be on parabolic equations, and we will show how the problems at hand have solutions that seem…
This is a concise introduction to the theory of Lie groupoids, with emphasis in their role as models for stacks. After some preliminaries, we review the foundations on Lie groupoids, and we carefully study equivalences and proper groupoids.…
A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation, by means of its differential representation. The package provides functions which enable us to solve the determining…
In this paper we describe the the category of Lie algebras of group algebras and the category of Plesken Lie algebras and explore the categorical relations between them. Further we provide the examples of the Lie algebra of the group…
A review is given of some recently obtained results on analytic contractions of Lie algebras and Lie groups and their applications to special function theory.
We study the class of 3-dimensional nonlinear 2-hessian equations mentioned in the text. We perform preliminary group classification on 2-hessian equation. In fact, we find additional equivalence transformation on the space (x,y,z,u,f),…
In these lectures notes I discuss the Linearization Theorem for Lie groupoids, and its relation to the various classical linearization theorems for submersions, foliations and group actions. In particular, I explain in some detail the…