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Direct Limits of Infinite-Dimensional Lie Groups

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Developments and Trends in Infinite-Dimensional Lie Theory

Part of the book series: Progress in Mathematics ((PM,volume 288))

Summary

Many infinite-dimensional Lie groups G of interest can be expressed as the union G = ∪n∈ℕ G n of an ascending sequence \(G_{1} \subseteq G_{2} \subseteq \cdots \) of (finite- or infinite-dimensional) Lie groups. In this survey article, we compile general results concerning such ascending unions, describe the main classes of examples and explain what the general theory tells us about them.

2000 Mathematics Subject Classifications: Primary 22E65. Secondary 26E15, 46A13, 46G20, 46T05, 46T20, 46T25, 54B35, 54D50, 55Q10, 58B05, 58D05.

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  1. Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098, Paderborn, Germany

    Helge Glöckner

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    Karl-Hermann Neeb

  2. University of Alberta, Department of Mathematical Sciences, Edmonton, T6G 2G1, Alberta, Canada

    Arturo Pianzola

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Glöckner, H. (2011). Direct Limits of Infinite-Dimensional Lie Groups. In: Neeb, KH., Pianzola, A. (eds) Developments and Trends in Infinite-Dimensional Lie Theory. Progress in Mathematics, vol 288. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4741-4_8

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