I'm trying to show that the composition of two Lorentz boosts produces a boost and a rotation using the generators from the Lorentz Group. If $\vec{K}$ denotes the Lorentz Boost generators and $\vec{S}$ denotes the rotation generators then two successive Lorentz Boosts in the $x$- and then $y$-directions is given by $$e^{-\xi_yK_y}e^{-\xi_xK_x}$$ How do I go on from here to prove the result is another boost and a rotation? I know I have to make use of the commutator $$[K_i,K_j]=-\epsilon_{ijk}S_k$$ but I'm not sure how to proceed.
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