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Abstract

We describe a setting of infinite-dimensional smooth (resp., analytic) Lie groups modelled on arbitrary, not necessarily sequentially complete, locally convex spaces, generalizing the framework of Lie theory formulated in [R. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. 7 (1982), 65–222] for Fréchet modelling spaces and in [J. Milnor, Remarks on infinite-dimensional Lie groups, in: B. DeWitt and R. Stora (eds.), Relativity, Groups and Topology II, North-Holland, 1983] for sequentially complete modelling spaces. Our studies were dictated by the needs of infinite-dimensional Lie theory in the context of the existence problem of universal complexifications. We explain why satisfactory results in this area can only be obtained if the requirement of sequential completeness is abandoned.