  We discuss some general aspects of commutators of local operators in
Lorentzian CFTs, which can be obtained from a suitable analytic continuation of
the Euclidean operator product expansion (OPE). Commutators only make sense as
distributions, and care has to be taken to extract the right distribution from
the OPE. We provide explicit computations in two and four-dimensional CFTs,
focusing mainly on commutators of components of the stress-tensor. We rederive
several familiar results, such as the canonical commutation relations of free
field theory, the local form of the Poincar\'e algebra, and the Virasoro
algebra of two-dimensional CFT. We then consider commutators of light-ray
operators built from the stress-tensor. Using simplifying features of the light
sheet limit in four-dimensional CFT we provide a direct computation of the BMS
algebra formed by a specific set of light-ray operators in theories with no
light scalar conformal primaries. In four-dimensional CFT we define a new
infinite set of light-ray operators constructed from the stress-tensor, which
all have well-defined matrix elements. These are a direct generalization of the
two-dimensional Virasoro light-ray operators that are obtained from a conformal
embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity
conditions similar to their two-dimensional analogues, and also share the
property that a semi-infinite subset annihilates the vacuum.
