Journal article
On the Morita Equivalence of Tensor Algebras
Proceedings of the London Mathematical Society, Vol.81(1), pp.113-168
07/2000
DOI: 10.1112/S0024611500012405
Abstract
We develop a notion of Morita equivalence for general C*-correspondences over C*-algebras. We show that if two correspondences are Morita equivalent, then the tensor algebras built from them are strongly Morita equivalent in the sense developed by Blecher, Muhly and Paulsen. Also, the Toeplitz algebras are strongly Morita equivalent in the sense of Rieffel, as are the Cuntz–Pimsner algebras. Conversely, if the tensor algebras are strongly Morita equivalent, and if the correspondences are aperiodic in a fashion that generalizes the notion of aperiodicity for automorphisms of C*-algebras, then the correspondences are Morita equivalent. This generalizes a venerated theorem of Arveson on algebraic conjugacy invariants for ergodic, measure-preserving transformations. The notion of aperiodicity, which also generalizes the concept of full Connes spectrum for automorphisms, is explored; its role in the ideal theory of tensor algebras and in the theory of their automorphisms is investigated. 1991 Mathematics Subject Classification: 46H10, 46H20, 46H99, 46M99, 47D15, 47D25.
Details
- Title: Subtitle
- On the Morita Equivalence of Tensor Algebras
- Creators
- Paul S Muhly - Department of Mathematics, University of Iowa Iowa City, IA 52242, USA; muhly@math.uiowa.eduBaruch Solel - Department of Mathematics, The Technion 32000, Haifa, Israel; mabaruch@techunix.technion.ac.il
- Resource Type
- Journal article
- Publication Details
- Proceedings of the London Mathematical Society, Vol.81(1), pp.113-168
- Publisher
- Oxford University Press
- DOI
- 10.1112/S0024611500012405
- ISSN
- 0024-6115
- eISSN
- 1460-244X
- Language
- English
- Date published
- 07/2000
- Academic Unit
- Mathematics; Statistics and Actuarial Science
- Record Identifier
- 9984083822102771
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