# 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 \(e^A\)