Philipp Schmitt

Real Nullstellensatz for nilpotent Lie algebras

We prove a real Nullstellensatz for the universal enveloping algebra U(g) of a nilpotent finite-dimensional real Lie algebra g: An ideal of U(g) is real if and only if it is the intersection of kernels of irreducible integrable *-representations of U(g) by (in general unbounded) operators on a Hilbert space. For this,...