  Starting from a N=1 scalar supermultiplet in 2+1 dimensions, we demonstrate
explicitly the appearance of induced N=1 vector and scalar supermultiplets of
composite operators made out of the fundamental supersymmetric constituents. We
discuss an extension to a N=2 superalgebra with central extension, due to the
existence of topological currents in 2+1 dimensions. As a specific model we
consider a supersymmetric $CP^1$ $\sigma$-model as the constituent theory, and
discuss the relevance of these results for an effective description of the
infrared dynamics of planar high-temperature superconducting condensed matter
models with quasiparticle excitations near nodal points of their Fermi surface.
