  We present higher-spin algebras containing a Poincar\'e subalgebra and with
the same set of generators as the Lie algebras that are relevant to Vasiliev's
equations in any space-time dimension $D \geq 3$. Given these properties, they
can be considered either as candidate rigid symmetries for higher-spin gauge
theories in Minkowski space or as Carrollian conformal higher-spin symmetries
in one less dimension. We build these Lie algebras as quotients of the
universal enveloping algebra of $iso(1,D-1)$ and we show how to recover them as
In\"on\"u-Wigner contractions of the rigid symmetries of higher-spin gauge
theories in Anti de Sitter space or, equivalently, of relativistic conformal
higher-spin symmetries. We use the same techniques to also define higher-spin
algebras with the same set of generators and containing a Galilean conformal
subalgebra, to be interpreted as non-relativistic limits of the conformal
symmetries of a free scalar field. We begin by showing that the known
flat-space higher-spin algebras in three dimensions can be obtained as
quotients of the universal enveloping algebra of $iso(1,2)$ and then we extend
the analysis along the same lines to a generic number of space-time dimensions.
We also discuss the peculiarities that emerge for $D=5$.
