The generators of a continuous group form a basis of a lie algebra. Properties:

• lie algebra == vector space with dim = dim of corresponding group.
• lie algebra closed under commutation [ , ].

[Xi,Xj]=ifijkXk

where fijk = structure constants of the lie algebra.

For a compact Lie group:

• fijk=-fjik always
• there exists a basis of generators s.t. fijk=eijk= antisymmetric tensor
• Jacobi identity => Sum(lm,fijlflkm+cyclic permutations)=0
• Xi's are hermitian

A lie algebra can correspond to multiple groups. Examples:
SU(4) and SO(6)
SU(2) and SO(3)
SO(4) and SU(2)xSU(2)
SO(5) and SP(2)