Extending Lie Group Theory to Locally Compact Groups and Beyond.
by
Karl H. Hofmann
Technische-Universität Darmstadt

In harmonic analysis, the existence of Haar measure makes the category of locally compact groups very amenable to scrutiny. For the purposes of structure theory, this category is defective by not being complete: It is not closed under the formation of arbitrary products nor by passing to the topological vector spaces underlying the Lie algebras of locally compact groups. Sid Morris and I plan a monograph on "The Structure of Locally Compact Groups and Pro-Lie Groups", in which we show that a satisfactory supercategory of the category of locally compact groups can be exhibited. The lecture shall explain why this is so and describe some of the aspects of this category.

Date received: March 27, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagw-07.