K3 surfaces over number fields and the Mumford–Tate conjecture

Given a K3 surface $S$ over a number field $k$, the author computes the semisimple part of the Lie algebra of the image of the $l$-adic representation in 2-dimensional cohomology of $S$ under the condition that $\operatorname{rank}NS(S\otimes_k\bar k)\ne2$.