How Does Knowing a Lie Algebra Inform Us About Its Corresponding Lie Group?

[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?

 

[Omega137]

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?

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