  We derive a necessary and sufficient condition for Poincar\'e Lie
superalgebras in any dimension and signature to be isomorphic. This reduces the
classification problem, up to certain discrete operations, to classifying the
orbits of the Schur group on the vector space of superbrackets. We then
classify four-dimensional ${\cal N}=2$ supersymmetry algebras, which are found
to be unique in Euclidean and in neutral signature, while in Lorentz signature
there exist two algebras with R-symmetry groups $\mathrm{U}(2)$ and
$\mathrm{U(}1,1)$, respectively. By dimensional reduction we construct two off
shell vector multiplet representations for each possible signature, and find
that the corresponding Lagrangians always have a different relative sign
between the scalar and the Maxwell term. In Lorentzian signature this is
related to the existence of two non-isomorphic algebras, while in Euclidean and
neutral signature the two theories are related by a local field redefinition
which implements an isomorphism between the underlying supersymmetry algebras.
