Stable isomorphism and strong Morita equivalence of C^∗-algebras

Lawrence Gerald Brown, Philip Palmer Green and Marc Aristide Rieffel

Vol. 71 (1977), No. 2, 349–363

DOI: 10.2140/pjm.1977.71.349

Abstract

We show that if A and B are C^∗-algebras which possess countable approximate identities, then A and B are stably isomorphic if and only if they are strongly Morita equivalent. By considering Breuer ideals, we show that this may fail in the absence of countable approximate identities. Finally we discuss the Picard groups of C^∗-algebras, especially for stable algebras.

Mathematical Subject Classification 2000

Primary: 46L05

Milestones

Received: 16 February 1977

Published: 1 August 1977