05 May 2014 No Comments

## Chapter 11: Lie Groups as Manifolds: The Conventional Lie Group Definition 2

Having proven that the concept of a connected Lie group as defined by axioms 1 through 5 leads to the modern concept of a Lie group as an analytic manifold wherein the group operations are analytic and thus that the two conceptions of the Lie group notion are the same, we shall now tell the […]

07 May 2014 No Comments

## Chapter 12: The Lie Correspondence: Lie’s Analogies with Galois Theory

In the early days of Lie theory after 1870, Sophus Lie imagined a Galois theory for continuous groups and strove for a theory along these lines. Indeed there is a beautiful bijection known as the Lie Correspondence that we are about to study that is in many ways a realisation of Lie’s original forethought, although […]

by Rod Vance in Lie Groups: What They Are, Lie Theory, Part 1: The Local View Tags: Galois Theory, Group Topology, Lie Correspondence