Discussing the mathematical formalism of generators (Lorentz Group)

[JD_PM]

Rotations or non-rotations, by the object $(M_{\alpha \beta})^{\mu}{}_{\nu}$, we always mean the $(\mu\nu)$ matrix elements of the matrix $M_{\alpha \beta}$.

Alright, so the upper index refers to rows and the lower to columns always. Thanks for the clarification.

 

[JD_PM]

[...] the Baker-Campbell-Hausdorf formula [...]

I've found a reliable source about the Baker-Campbell-Hausdorf formula: problem 3 here. The solution is here .