Book Review: Lie groups: An introduction through linear groups

Introduction to Lie groups

Lie Groups and Mechanics, an Introduction

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 in a third section we apply these methods for the diffeomorphism group of the circle with two particular examples: the Burger equation and the Camassa-Holm eq...

Linear ODEs in Lie groups

The solution of Y 0 = A(t)Y; Y (0) = Y0, where Y is in a matrical Lie group G and A(t) is in the Lie algebra of G, is discussed in this article. The basis of our approach are generalized iterated commutators. In that manner we can approximate the solution to an arbitrarily high order. The exact solution is given as an infinite series of commutators and order conditions are studied by using bina...

Introduction to Representations Theory of Lie Groups

The purpose of this notes is twofold. The first goal is to give a quick answer to the question “What is representation theory about?” To answer this, we will show by examples what are the most important results of this theory, and the problems that it is trying to solve. To make the answer short we will not develop all the formal details of the theory and we will give preference to examples ove...

Matrix Groups : An Introduction to Lie Group Theory

The elementary theory of Lie groups has something in common with precalculus: One wants to get past it in order to get on with the beautiful and powerful theory that follows, as well as the applications. With precalculus the theory that follows is built around calculus and its fundamental theorem, extending into calculus of several variables and having profound applications through the subject ...