Lie Groups of Measurable Mappings

Canadian Journal of Mathematics

Volumn 55, Issue 5, 2003, Pages 969-999

  Glöckner, Helge ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142153695     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-2003-039-9     Document Type: Article

References (37)

1. S. Albeverio, R. J. Høegh-Krohn, J. A. Marion, D. H. Testard and B. S. Torrésani, Noncommutative Distributions. Marcel Dekker, 1993.
2. A. Bastiani, Applications différentiables et variétés différentiables de dimension infinie. J. Analyse Math. 13(1964), 1-114.
3. H. Bauer, Maß- und Integrationstheorie. 2nd edition, de Gruyter, 1992.
4. A. Bloch, M. O. El Hadrami, H. Flaschka and T. S. Ratiu, Maximal tori of some symplectomorphism groups and applications to convexity. In: Deformation Theory and Symplectic Geometry (Ascona, 1996), Math. Phys. Stud. 20, Kluwer, Dordrecht, 1997, 201-222.
5. J. Bochnak and J. Siciak, Analytic functions in topological vector spaces. Studia Math. 39(1971), 77-112.
6. H. Boseck, G. Czichowski and K.-P. Rudolph, Analysis on Topological Groups - General Lie Theory. Teubner, Leipzig, 1981.
7. N. Bourbaki, Topological Vector Spaces, Chapters 1-5. Springer-Verlag, 1987.
8. _, Lie Groups and Lie Algebras, Chapters 1-3. Springer-Verlag, 1989.
9. R. Engelking, General Topology. Heldermann-Verlag, Berlin, 1989.
10. H. Glöckner, Infinite-dimensional Lie groups without completeness restrictions. In: Geometry and Analysis on Finite- and Infinite-Dimensional Lie Groups (eds. A. Strasburger et al.), Banach Center Publications, Vol. 55, Warsaw, 2002, 43-59.
11. _, Algebras whose groups of units are Lie groups. Studia Math. 153(2002), 147-177.
12. _, Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups. J. Funct. Anal. 194(2002), 347-409.
13. _, Direct limit Lie groups and manifolds. Math. J. Kyoto Univ. 43(2003), in print.
14. _, Discontinuous non-linear mappings on locally convex direct limits. Submitted.
15. _, Patched locally convex spaces, almost local mappings, and diffeomorphism groups of non-compact manifolds. In preparation.
16. _, Lie groups over non-discrete topological fields. In preparation.
17. R. Hamilton, The inverse function theorem of Nash and Moser. Bull. Amer. Math. Soc. 7(1982), 65-222.
18. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis 1. Springer-Verlag, 1979.
19. E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups. Amer. Math. Soc., Providence, 1957.
20. N. Kamran and T. Robart, On the parametrization problem of Lie pseudogroups of infinite type. C. R. Acad. Sci. Paris Sér. I Math. 331(2000), 899-903.
21. _, A manifold structure for analytic isotropy Lie pseudogroups of infinite type. J. Lie Theory 11(2001), 57-80.
22. H. H. Keller, Differential Calculus in Locally Convex Spaces. Springer-Verlag, Berlin, 1974.
23. A. Kriegl and P. W. Michor, The Convenient Setting of Global Analysis. Amer. Math. Soc., Providence R. I., 1997.
24. J. Milnor, Remarks on infinite dimensional Lie groups. In: Relativity, Groups and Topology II (eds. B. DeWitt and R. Stora), North-Holland, 1983, 1008-1057.
25. L. Natarajan, E. Rodríguez-Carrington and J. A. Wolf, Differentiable structure for direct limit groups. Lett. Math. Phys. 23(1991), 99-109.
26. _, Locally convex Lie groups. Nova J. Algebra Geom. (1) 2(1993), 59-87.
27. _, New classes of infinite-dimensional Lie groups. In: Algebraic Groups and their Generalizations, Proc. Sympos. Pure Math. 56, Part II, 1994, 377-392.
28. _, The Bott-Borel-Weil Theorem for direct limit groups. Trans. Amer. Math. Soc. 353(2001), 4583-4622.
29. K.-H. Neeb, Infinite-dimensional groups and their representations. In: Infinite-dimensional Kähler manifolds (eds. A. T. Huckleberry and T. Wurzbacher), Birkhäuser Verlag, 2001, 131-178.
30. _, Central extensions of infinite-dimensional Lie groups. Ann. Inst. Fourier (Grenoble) 52(2002), 1365-1442.
31. A. Pressley and G. B. Segal, Loop Groups. Clarendon Press, Oxford, 1986.
32. T. Robart, Sur l'intégrabilité des sous-algèbres de Lie en dimension infine. Canad. J. Math. 49(1997), 820-839.
33. W. Rudin, Real and Complex Analysis. McGraw-Hill, 1987.
34. H. H. Schaefer, Topological Vector Spaces. Springer-Verlag, 1971.
35. H. Schubert, Topologie. Teubner-Verlag, 1964.
36. N. Tatsuuma, H. Shimomura and T. Hirai, On group topologies and unitary representations on inductive limits of topological groups and the case of the group of diffeomorphisms. Math. J. Kyoto Univ. 38(1998), 551-578.
37. E. G. F. Thomas, Calculus on locally convex spaces. Preprint W-9604, Groningen Univ., 1996.