Isomorphism of Hilbert modules over stably finite C*-algebras

By N. Brown, A. Ciuperca. 2008

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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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0df37ba591249b198c8bc0de7a8a4ea0d8712584