A complex semigroup approach to group algebras of infinite dimensional Lie groups |
| |
Authors: | Karl-Hermann Neeb |
| |
Institution: | 1. Fachbereich Mathematik, Technische Universit?t, Schlossgartenstr. 7, 64289, Darmstadt, Germany
|
| |
Abstract: | A host algebra of a topological group G is a C
*-algebra whose representations are in one-to-one correspondence with certain continuous unitary representations of G. In this paper we present an approach to host algebras for infinite dimensional Lie groups which is based on complex involutive
semigroups. Any locally bounded absolute value α on such a semigroup S leads in a natural way to a C
*-algebra C
*(S,α), and we describe a setting which permits us to conclude that this C
*-algebra is a host algebra for a Lie group G. We further explain how to attach to any such host algebra an invariant weak-*-closed convex set in the dual of the Lie algebra
of G enjoying certain nice convex geometric properties. If G is the additive group of a locally convex space, we describe all host algebras arising this way. The general non-commutative
case is left for the future.
To K.H. Hofmann on the occasion of his 75th birthday |
| |
Keywords: | Complex semigroup Infinite dimensional Lie group Host algebra Multiplier algebra Unitary representation |
本文献已被 SpringerLink 等数据库收录! |
|