
Journal of Lie Theory 11 (2001), No. 1, 057080 Copyright Heldermann Verlag 2001 A Manifold Structure for Analytic Isotropy Lie Pseudogroups of Infinite Type Niky Kamran Dept. of Mathematics, McGill University, Montreal, QC H3A 2K6, Canada Thierry Robart Dept. of Mathematics, Howard University, Washington, DC 20059, U.S.A. We give the solution of Lie's third fundamental problem for the class of infinite dimensional Lie algebras corresponding to the isotropy subpseudogroups of the flat transitive analytic Lie pseudogroups of infinite type. The associated Lie groups are regular Gateauxanalytic infinitedimensional Lie groups whose compatible manifold structure is modelled on locally convex topological vector spaces (countable inductive limits of Banach spaces) of vector fields by charts involving countable products exponential mappings. This structure theorem is applied to the local automorphisms pseudogroups of Poisson, symplectic, contact and unimodular structures. In particular the local analytic LiePoisson algebra associated to any finite dimensional real Lie algebra is shown to be integrable into a unique connected and simply connected regular infinitedimensional Gateauxanalytic Lie group. [ Fulltextpdf (276 KB)] 