On quantales that classify C*-algebras
Operator Algebras
2007-05-23 v1 Category Theory
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.math/0404001,
title = {On quantales that classify C*-algebras},
author = {David Kruml and Pedro Resende},
journal= {arXiv preprint arXiv:math/0404001},
year = {2007}
}