On quantales that classify C*-algebras

David Kruml; Pedro Resende

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On quantales that classify C*-algebras

David Kruml·Pedro Resende

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Abstract

The functor Max of Mulvey assigns to each unital C*-algebra A the unital involutive quantale Max A of closed linear subspaces of A, and it has been remarked that it classifies unital C*-algebras up to *-isomorphism. In this paper we provide a proof of this and of the stronger fact that for every isomorphism u : Max A -> Max B of unital involutive quantales there is a *-isomorphism u' : A -> B such that Max u' coincides with u when restricted to the left-sided elements of Max A. But we also show that isomorphisms u : Max A -> Max B may exist for which no isomorphism v : A -> B is such that Max v = u.

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BibTeX RIS

David Kruml, Pedro Resende. 2004-03-31. On quantales that classify C*-algebras. https://arxiv.org/abs/math/0404001

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