Integrable and proper actions on C*-algebras, and square-integrable representations of groups

Details Integrable and proper actions on C*-algebras, and square-integrable representations of groups Integrable and proper actions on C*-algebras, and square-integrable representations of groups

1998-09-17

arxiv.org/abs/math/9809098v2

Expositiones Math. 22 (2004) 1-53

Mathematics

Operator Algebras

49 pages, AMSTEX. Major changes made to the discussion of generalized fixed-point algebras, to reflect discoveries by Exel des

Scientific paper

We propose a definition of what should be meant by a {\it proper} action of a locally compact group on a C*-algebra. We show that when the C*-algebra is commutative this definition exactly captures the usual notion of a proper action on a locally compact space. We then discuss how one might define a {\it generalized fixed-point algebra}. The goal is to show that the generalized fixed-point algebra is strongly Morita equivalent to an ideal in the crossed product algebra, as happens in the commutative case. We show that one candidate gives the desired algebra when the C*-algebra is commutative. But very recently Exel has shown that this candidate is too big in general. Finally, we consider in detail the application of these ideas to actions of a locally compact group on the algebra of compact operators (necessarily coming from unitary representations), and show that this gives an attractive view of the subject of square-integrable representations.

Affiliated with

Also associated with

No associations

Rating

Integrable and proper actions on C*-algebras, and square-integrable representations of groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Integrable and proper actions on C*-algebras, and square-integrable representations of groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Integrable and proper actions on C*-algebras, and square-integrable representations of groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-458439