# Lie group and Lie algebra

1. Jan 7, 2010

### paweld

What can we tell about Lie group if we know its Lie algebra.
Let's consider the following example: we have three elements
of Lie algebra which fulfill condition $$[L_i,L_j]=i \epsilon_{ijk}L_k$$.
The corresponding Lie group is SU(2) or SO(3) (are there any other?).
Does anyone know what condition on Lie group is imposed by Lie algebra?

2. Jan 10, 2010

### Omega137

There is only one simply connected Lie Group corresponding to a semisimple Lie Algebra; (up to an isomorphism).