Differentiable vectors and unitary representations of Frechet-Lie supergroups

Abstract

For a locally convex Lie group with the Trotter property, we prove that the space of k-times differentiable vectors of a unitary representation is equal to the intersection of domains of k-fold products of the Lie algebra action. The result also holds for continuous representations of locally exponential groups on metrizable locally convex spaces. As an application, we extend a key stability theorem in the representation theory of Lie supergroups beyond the Banach case.

arXiv commentAccepted version (to appear in Mathematische Zeitschrift)

References in corpus (1)

• Lie Group Structures on Symmetry Groups of Principal Bundles

Cited by in corpus (3)

• The Lie group of bisections of a Lie groupoid
• (Re)constructing Lie groupoids from their bisections and applications to prequantisation
• Lie Theory for Asymptotic Symmetries in General Relativity: The NU Group