generators of lie groups
1. generators
- even if there are infinite number of elements in the lie group, there can still be finite generators
- you can take
- a similarity transform (see matrix similarity) \(UXU^{-1}\)
- direct product
- kronecker sum
of a generator set and the resulting set will also generate a lie group
2. from generators to representations
- elements of the lie group (representation) take the form \(e^A\)