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 . 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 . 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 . 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.
- AMS (MOS) subject classification (1980): 58B25
- Regular Fréchet-Lie group
ASJC Scopus subject areas
- Applied Mathematics