Acceptable Compact Lie Groups

Compact Lie Groups

The first half of the paper presents the basic definitions and results necessary for investigating Lie groups. The primary examples come from the matrix groups. The second half deals with representation theory of groups, particularly compact groups. The end result is the Peter-Weyl theorem.

Lie Groups and p-Compact Groups

A p-compact group is the homotopical ghost of a compact Lie group; it is the residue that remains after the geometry and algebra have been stripped away. This paper sketches the theory of p-compact groups, with the intention of illustrating the fact that many classical structural properties of compact Lie groups depend only on homotopy theoretic considerations. 1 From compact Lie groups to p-co...

Probability on Compact Lie Groups

Central Multiplier Theorems for Compact Lie Groups

The purpose of this note is to describe how central multiplier theorems for compact Lie groups can be reduced to corresponding results on a maximal torus. We shall show that every multiplier theorem for multiple Fourier series gives rise to a corresponding theorem for such groups and, also, for expansions in terms of special functions. We use the notation and terminology of N. J. Weiss [4]. Let...

Some Model Theory of Compact Lie Groups

We consider questions of first order definability in a compact Lie group G . Our main result is that if such G is simple (and centerless) then the Lie group structure of G is first order definable from the abstract group structure. Along the way we also show (i) if G is non-Abelian and connected then a copy of the field R is interpretable, in (G, •), and (ii) any "1-dimensional" field interpret...