  We investigate the algebra of vector fields on the sphere. First, we find
that linear deformations of this algebra are obstructed under reasonable
conditions. In particular, we show that $hs[\lambda]$, the one-parameter
deformation of the algebra of area-preserving vector fields, does not extend to
the entire algebra. Next, we study some non-central extensions through the
embedding of $\mathfrak{v}\mathfrak{e}\mathfrak{c}\mathfrak{t}(S^2)$ into
$\mathfrak{v}\mathfrak{e}\mathfrak{c}\mathfrak{t}(\mathbb{C}^*)$. For the
latter, we discuss a three parameter family of non-central extensions which
contains the symmetry algebra of asymptotically flat and asymptotically
Friedmann spacetimes at future null infinity, admitting a simple free field
realization.
