Components of adjoint representations

[synoe]

In the way of defining the adjoint representation,
$$\mathrm{ad}_XY=[X,Y],$$
where $X,Y$ are elements of a Lie algebra, how to determine the components of its representation, which equals to the structure constant?

 

[ChrisVer]

http://en.wikipedia.org/wiki/Adjoint_representation_of_a_Lie_algebra#Structure_constants

If you need more information, you could ask... but it's just writing everything in matrix form/components, since the adjoint is a linear mapping...