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

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 C-K(r)(M, G):= {gamma is an element of C-r(M, G):\(M\K) = 1}, for every BCH-Lie group G, second countable finite-dimensional smooth manifold M, compact subset K of M, and 0less than or equal torless than or equal toinfinity. Also the corresponding test function groups D-r(M,G)=boolean ORK C-K(r)(M, G) are BCH-Lie groups. (C) 2002 Elsevier Science (USA).