On locally compact quantum groups whose algebras are factors

摘要

In this paper we are interested in examples of locally compact quantum groups (M, A) such that both von Neumann algebras, M and the dual (M) over cap, are factors. There is a lot of known examples such that (M, (M) over cap) are respectively of type (I-infinity, I-infinity) but there is no example with factors of other types. We construct new examples of type (I-infinity, II infinity), (II infinity, II infinity) and (III lambda, III lambda) for each lambda is an element of [0, 1]. We also show that there is no such example with M or (M) over cap a finite factor. (c) 2006 Elsevier Inc. All rights reserved.