Isomorphism of Hilbert modules over stably finite C-algebras |
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Authors: | Nathanial P Brown Alin Ciuperca |
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Institution: | a Department of Mathematics, Penn State University, State College, PA 16802, USA b Fields Institute, 222 College Street, Toronto, Ontario, Canada, M5T 3J1 |
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Abstract: | It is shown that if A is a stably finite C∗-algebra and E is a countably generated Hilbert A-module, then E gives rise to a compact element of the Cuntz semigroup if and only if E is algebraically finitely generated and projective. It follows that if E and F are equivalent in the sense of Coward, Elliott and Ivanescu (CEI) and E is algebraically finitely generated and projective, then E and F are isomorphic. In contrast to this, we exhibit two CEI-equivalent Hilbert modules over a stably finite C∗-algebra that are not isomorphic. |
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Keywords: | C&lowast -algebras Hilbert modules Cuntz semigroup compact |
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