For an infinite-dimensional Lie group modeled on a locally convex Lie algebra , we prove that every smooth projective unitary representation of corresponds to a smooth linear unitary representation of a Lie group extension of . (The main point is the smooth structure on .) For infinite-dimensional Lie groups which are -connected, regular, and modeled on a barreled Lie algebra , we characterize the unitary -representations which integrate to . Combining these results, we give a precise formulation of the correspondence between smooth projective unitary representations of , smooth linear unitary representations of , and the appropriate unitary representations of its Lie algebra .
"Projective unitary representations of infinite-dimensional Lie groups." Kyoto J. Math. 59 (2) 293 - 341, June 2019. https://doi.org/10.1215/21562261-2018-0016