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Infinite-dimensional Lie groups without completeness restrictions. (English) Zbl 1020.58009
Strasburger, Aleksander (ed.) et al., Geometry and analysis on finite- and infinite-dimensional Lie groups. Proceedings of the workshop on Lie groups and Lie algebras, Bȩdlewo, Poland, September 4-15, 2000. Warszawa: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 55, 43-59 (2002).
As a generalization of the Lie theory for Fréchet modelling spaces [see V. M. Gol’dshteĭn, V. I. Kuz’minov and I. A. Shvedov, Sib. Mat. Zh. 23, No. 2, 16-30, 215 (1982; Zbl 0522.58001)] and for sequentially complete modelling spaces [see J. Milnor, Remarks on infinite-dimensional Lie groups, Relativité, groupes et topologie II, Les Houches Éc. d’Eté Phys. Théor., Sess. 40, 1983, 1007-1057 (1984; Zbl 0594.22009)] the infinite-dimensional smooth (and analytic) Lie groups on arbitrary, not-necessarily sequentially complete, locally convex spaces are described. The study is dicted by the needs of infinite-dimensional Lie theory in the context of the existence problem of universal complexification. The problem is solved for Baker-Campbell-Hausdorff Lie groups.
For the entire collection see [Zbl 0989.00033].

MSC:
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
46T20 Continuous and differentiable maps in nonlinear functional analysis
46T25 Holomorphic maps in nonlinear functional analysis
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