  In this paper we introduce the systematic study of invariant functions and
equivariant mappings defined on Minkowski space under the action of the Lorentz
group. We adapt some known results from the orthogonal group acting on the
Euclidean space to the Lorentz group acting on the Minkowski space. In
addition, an algorithm is given to compute generators of the ring of functions
that are invariant under an important class of Lorentz subgroups, namely when
these are generated by involutions, which is also useful to compute
equivariants. Furthermore, general results on invariant subspaces of the
Minkowski space are presented, with a characterization of invariant lines and
planes in the two lowest dimensions.
