### 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 language | English |
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Pages (from-to) | 71-106 |

Number of pages | 36 |

Journal | Acta Applicandae Mathematicae |

Volume | 3 |

Issue number | 1 |

DOIs | |

Publication status | Published - 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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## Cite this

*Acta Applicandae Mathematicae*,

*3*(1), 71-106. https://doi.org/10.1007/BF01438267