The theory of infinite-dimensional lie groups and its applications

Osamu Kobayashi, Akira Yoshioka, Yoshiaki Maeda, Hideki Omori

    Research output: Contribution to journalReview article

    12 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)71-106
    Number of pages36
    JournalActa Applicandae Mathematicae
    Volume3
    Issue number1
    DOIs
    Publication statusPublished - 1985 Jan 1

    Keywords

    • AMS (MOS) subject classification (1980): 58B25
    • Regular Fréchet-Lie group
    • enlargeability

    ASJC Scopus subject areas

    • Applied Mathematics

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