  Meta-conformal transformations are constructed as sets of time-space
transformations which are not angle-preserving but contain time- and space
translations, time-space dilatations with dynamical exponent ${z}=1$ and whose
Lie algebras contain conformal Lie algebras as sub-algebras. They act as
dynamical symmetries of the linear transport equation in $d$ spatial
dimensions. For $d=1$ spatial dimensions, meta-conformal transformations
constitute new representations of the conformal Lie algebras, while for $d\ne
1$ their algebraic structure is different. Infinite-dimensional Lie algebras of
meta-conformal transformations are explicitly constructed for $d=1$ and $d=2$
and they are shown to be isomorphic to the direct sum of either two or three
centre-less Virasoro algebras, respectively. The form of co-variant two-point
correlators is derived. An application to the directed Glauber-Ising chain with
spatially long-ranged initial conditions is described.
