Lie group structures on symmetry groups of principal bundles

Journal of Functional Analysis

Volumn 251, Issue 1, 2007, Pages 254-288

  Wockel, Christoph ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

Automorphism group; Gauge group; Infinite dimensional Lie group; Kac Moody algebra; Kac Moody group; Mapping group

Indexed keywords

EID: 34548016778     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2007.05.016     Document Type: Article

References (30)

1. Abbati M.C., Cirelli R., and Manià A. The orbit space of the action of gauge transformation group on connections. J. Geom. Phys. 6 (1989) 537-557
2. Abbati M.C., Cirelli R., Manià A., and Michor P.W. The Lie group of automorphisms of a principal bundle. J. Geom. Phys. 6 2 (1989) 215-235
3. Bourbaki N. General Topology. Elem. Math. (Berlin) (1989), Springer-Verlag, Berlin
4. Bourbaki N. Lie Groups and Lie Algebras (1989), Springer-Verlag
5. Bredon G.E. Introduction to Compact Transformation Groups. Pure Appl. Math. vol. 46 (1972), Academic Press, New York
6. Cirelli R., and Manià A. The group of gauge transformations as a Schwartz-Lie group. J. Math. Phys. 26 12 (1985) 3036-3041
7. Glöckner H. Infinite-dimensional Lie groups without completeness restrictions. Geometry and Analysis on Finite- and Infinite-Dimensional Lie Groups. Bȩdlewo, 2000. Banach Center Publ. vol. 55 (2002), Polish Acad. Sci., Warsaw 43-59
8. Glöckner H. Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups. J. Funct. Anal. 194 (2002) 347-409
9. Glöckner H. Fundamentals of direct limit Lie theory. Compos. Math. 141 6 (2005) 1551-1577
10. H. Glöckner, Patched locally convex spaces, almost local mappings and diffeomorphism groups of non-compact manifolds, manuscript, 2006
11. Haller S., and Teichmann J. Smooth perfectness through decomposition of diffeomorphisms into fiber preserving ones. Ann. Global Anal. Geom. 23 1 (2003) 53-63
12. Haller S., and Teichmann J. Smooth perfectness for the group of diffeomorphisms. arXiv: (2004). math.DG/0409605
13. Kriegl A., and Michor P.W. The Convenient Setting of Global Analysis. Math. Surveys Monogr. vol. 53 (1997), Amer. Math. Soc., Providence, RI
14. Lang S. Fundamentals of Differential Geometry. Grad. Texts in Math. vol. 191 (1999), Springer-Verlag, New York
15. Leslie J.A. On a differential structure for the group of diffeomorphisms. Topology 6 (1967) 263-271
16. Lecomte P. Sur l'algèbre de Lie des sections d'un fibre en algèbres de Lie. Ann. Inst. Fourier (Grenoble) 30 4 (1980) 35-50
17. Michor P.W. Manifolds of Differentiable Mappings. Shiva Math. Ser. vol. 3 (1980), Shiva, Nantwich. http://www.mat.univie.ac.at/~michor/ out of print, online available from http://www.mat.univie.ac.at/~michor/
18. Milnor J. Remarks on infinite-dimensional Lie groups. Relativity, Groups and Topology, II. Les Houches, 1983 (1984), North-Holland, Amsterdam 1007-1057
19. Michor P.W. Gauge Theory for Fiber Bundles. Monogr. Textbooks Phys. Sci. Lecture Notes vol. 19 (1991), Bibliopolis, Naples
20. Neeb K.-H. Central extensions of infinite-dimensional Lie groups. Ann. Inst. Fourier (Grenoble) 52 5 (2002) 1365-1442
21. Neeb K.-H. Non-abelian extensions of infinite-dimensional Lie groups. Ann. Inst. Fourier (Grenoble) 57 1 (2007) 209-271
22. Neeb K.-H. Towards a Lie theory of locally convex groups. Jpn. J. Math. (N.S.) 1 12 (2006) 291-468
23. Omori H., Maeda Y., Yoshioka A., and Kobayashi O. On regular Fréchet-Lie groups. V. Several basic properties. Tokyo J. Math. 6 1 (1983) 39-64
24. Pressley A., and Segal G. Loop Groups. Oxford Math. Monogr./Oxford Sci. Publ. (1986), Clarendon/Oxford Univ. Press, New York
25. Steenrod N. The Topology of Fibre Bundles. Princeton Math. Ser. vol. 14 (1951), Princeton Univ. Press, Princeton, NJ
26. Wasserman A.G. Equivariant differential topology. Topology 8 (1969) 127-150
27. Wockel C. A generalisation of Steenrod's approximation theorem. arXiv: (2006). math.DG/0610252
28. C. Wockel, Infinite-dimensional Lie theory for gauge groups, Dissertation, Technische Universität Darmstadt, 2006
29. Wockel C. Smooth extensions and spaces of smooth and holomorphic mappings. J. Geom. Symmetry Phys. 5 (2006) 118-126
30. C. Wockel, The Samelson product and rational homotopy for gauge groups, Abh. Math. Sem. Univ. Hamburg (2007), in press