Lie group structures on groups of smooth and holomorphic maps on non-compact manifolds

We review the Pontryagin duality theory. A function from G to G' is called a homomorphism if it is continuous and preserves the group operation. B y the category of

is its group of components ; subgroup will always mean closed subgroup ; and cyclic group will mean a compact Lie group containing an element, called the generator, whose powers

In spite of the fact that the regularized lattice phase-space path integral representation for the representation independent propagator has been constructed by

L’accès aux archives de la revue « Cahiers de topologie et géométrie différentielle catégoriques » implique l’accord avec les conditions générales d’utilisation

We deduce that for G an infinite definably compact group definable in an o-minimal expansion of a field, G 00 is bi- interpretable with the disjoint union of a (possibly trivial)

G where a runs through (A, v) is called disjoint if the family of the spectral measures 03BC03B1 of Ua is disjoint (with respect to the given Borel.. measure v

By the classification theory of compact connected Lie groups there are only a finite number in each dimension.. In these references

According to the idea of a paper [20], one can construct irreducible nonlocal representations of the group of measurable G-valued func- tions on X, G being a Lie