Automorphisms of locally compact groups

Justin Peters and Terje Sund

Vol. 76 (1978), No. 1, 143–156

DOI: 10.2140/pjm.1978.76.143

Abstract

It is proved that for arbitrary locally compact groups G the automorphism group Aut (G) is a complete topological group. Several conditions equivalent to closedness of the group Int (G) of inner automorphisms are given, such as G admits no nontrivial central sequences. It is shown that Aut (G) is topologically embedded in the automorphism group Aut ℛ(G) of the group von Neumann algebra. However, closedness of Int ℛ(G) does not imply closedness of Int (G), nor conversely.

Mathematical Subject Classification 2000

Primary: 22D45

Milestones

Received: 29 April 1977

Revised: 30 September 1977

Published: 1 May 1978