Why Are Two Indices Used for the Generators of Lorentz and Poincare Groups?

[Bobhawke]

Just a quick question here: I was going through my notes and I noticed that the generators of both these groups are labeled two indices. I was wondering if there is any particular reason for this, since it seems to me that one index would work perfectly well.

Thanks

 

[humanino]

There is no more reason to attach 2 indices to a Lorentz transformation than to an ordinary 3D rotation, or a matrix in general. A rotation will be specified by angles between one axis (first index) and another axis (second index). If it pleases you, you can store them in a vector, but that is clumsy.