Lie group structures on quotient groups and universal complexifications for infinite-dimensional lie groups

Abstract

We characterize the existence of Lie group structures on quotient groups and the existence of universal complexifications for the class of Baker-Campbell-Hausdorff (BCH-) Lie groups, which subsumes all Banach-Lie groups and "linear" direct limit Lie groups, as well as the mapping groups CrK(M,G):= {γ ε Cr(M,G): γ\M\K=1}, for every BCH-Lie group G, second countable finite-dimensional smooth manifold M, compact subset K of M, and 0≤r≤∞. Also the corresponding test function groups Dr(M, G) = ∪K CrK(M, G) are BCH-Lie groups. © 2002 Elsevier Science (USA).