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The theory of infinite-dimensional lie groups and its applications

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Abstract

The purpose of this paper is to survey the theory of regular Fréchet-Lie groups developed in [1–10]. Such groups appear and are useful in symplectic geometry and the theory of primitive infinite groups of Lie and Cartan [11]. From the group theoretical standpoint, general relativistic mechanics is a more closed system than Newtonian mechanics. Quantized objects of these classical groups are closely related to the group of Fourier integral operators [12]. These can also be managed as regular Fréchet-Lie groups. However, there are many Fréchet-Lie algebras which are not the Lie algebras of regular Fréchet-Lie groups [13]. Thus, the enlargeability of the Poisson algebra is discussed in detail in this paper. Enlargeability is relevant to the global hypoellipticity [14, 15] of second-order differential operators.

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Authors and Affiliations

  1. Department of Mathematics, Keio University, 223, Hiyoshi, Yokohama, Japan

    Osamu Kobayashi

  2. Department of Mathematics, Tokyo Metropolitan University, Fukazwa, Setagaya, 158, Tokyo, Japan

    Akira Yoshioka

  3. Department of Mathematics, Keio University, 223, Hiyoshi, Yokohama, Japan

    Yoshiaki Maeda

  4. Department of Mathematics, Science University of Tokyo, 278, Noda, Chiba, Japan

    Hideki Omori

Authors
  1. Osamu Kobayashi
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  2. Akira Yoshioka
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  3. Yoshiaki Maeda
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  4. Hideki Omori
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Kobayashi, O., Yoshioka, A., Maeda, Y. et al. The theory of infinite-dimensional lie groups and its applications. Acta Appl Math 3, 71–106 (1985). https://doi.org/10.1007/BF01438267

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