arXiv subjects
Publications and source records attributed to Mihai Nicolae.
We introduce moment maps for continuous unitary representations of general topological groups. For solvable separable locally compact groups, we prove that the closure of the image of the moment map of any representation is convex.
We establish the exponential law for suitably topologies on spaces of vector-valued smooth functions on topological groups, where smoothness is defined by using differentiability along continuous one-parameter subgroups. As an application, we investigate the canonical correspondences between the universal enveloping algebra, the invariant local operators, and the convolution algebra of distributions supported at the unit element of any finite-dimensional Lie group, when one passes from finite-dimensional Lie groups to pre-Lie groups. The latter class includes for instance any locally compact groups, Banach-Lie groups, additive groups underlying locally convex vector spaces, and also mapping groups consisting of rapidly decreasing Lie group-valued functions.