ISSN:
1572-9036
Keywords:
58B25
;
Regular Fréchet-Lie group
;
enlargeability
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01438267
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