Euclidean supersymmetry and the many-instanton problem

There is no Hermitean supersymmetry in Euclidean four-space. The simplest supersymmetry has complex four-component spinorial parameters. We give its algebraic structure and the automorphisms of the algebra, as well as a representation in terms of fields and an invariant Lagrangian. The results are relevant to the counting and the construction of the solutions of the many-instanton problem.