10 Apr 2014 No Comments

## Chapter 1: Connected Lie Groups: The Grounding Axioms

Therefore, more formally, I propose the following definition comprising five axioms that, for me at least, is the least redundant, least cluttered, and which also works for general Lie groups whilst admitting techniques found in references like [Rossmann]. Hereafter we shall consider a group $\left(\G,\bullet\right)$. For shorthand we often write the product of two group […]

01 May 2014 No Comments

## Chapter 9: The Lie Group Topology

The group operation clones the topological and framing structure defined on $\Nid$ as discussed so far, so that every element in the Lie group can have its own local co-ordinates relative to some nearby reference point $\gamma \in \G$. Small variations in any element $\gamma \in \G$ of the group, i.e. derivatives, can be studied […]

by Rod Vance in Lie Groups: What They Are, Lie Theory, Part 1: The Local View Tags: Connectedness, Neigbourhood, Nucleus, Topology