Unitary embeddings of finite loop spaces

Abstract

In this paper we construct faithful representations of saturated fusion systems over discrete p-toral groups and use them to find conditions that guarantee the existence of unitary embeddings of p-local compact groups. These conditions hold for the Clark-Ewing and Aguadé-Zabrodsky p-compact groups as well as some exotic 3-local compact groups. We also show the existence of unitary embeddings of finite loop spaces.

29 pages, no figures. New Section 2 added. Section 6 corrected. Other small corrections and simplifications

References in corpus (3)

• The classification of 2-compact groups
• An algebraic model for finite loop spaces
• Spaces with Noetherian cohomology

Cited by in corpus (2)

• Vector bundles over classifying spaces of p-local finite groups and Benson-Carlson duality
• Local Gorenstein duality for cochains on spaces