## Chapter 3: The Lie Algebra of the Lie Group and Canonical Co-ordinates

We now turn to the Lie algebra, which we shall define in the same way as [Rossmann] does in the first chapter. (Lie Algebra of a Connected Lie Group): For a connected Lie group $(\G,\,\bullet)$ as defined by Axioms 1 through 5, the Lie algebra $\g$ is the set of all tangent vectors at the […]