Recovering the Elliott invariant from the Cuntz semigroup
نویسندگان
چکیده
منابع مشابه
Recovering the Elliott Invariant from the Cuntz Semigroup
Let A be a simple, separable C∗-algebra of stable rank one. We prove that the Cuntz semigroup of C(T, A) is determined by its Murray-von Neumann semigroup of projections and a certain semigroup of lower semicontinuous functions (with values in the Cuntz semigroup of A). This result has two consequences. First, specializing to the case that A is simple, finite, separable and Z-stable, this yield...
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A category is described to which the Cuntz semigroup belongs and as a functor into which it preserves inductive limits. 1. Recently, Toms in [26] used the refinement of the invariant K0 introduced by Cuntz almost thirty years ago in [4] to show that certain C*-algebras are not isomorphic. Anticipating the possible use of this invariant to establish isomorphism, we take the liberty of reporting ...
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Domain theory has its origins in Mathematics and Theoretical Computer Science. Mathematically it combines order and topology. Its central concepts have their origin in the idea of approximating ideal objects by their relatively finite or, more generally, relatively compact parts. The development of domain theory in recent years was mainly motivated by question in denotational semantics and the ...
متن کامل. O A ] 6 S ep 2 00 6 THE CUNTZ SEMIGROUP , THE ELLIOTT CONJECTURE , AND DIMENSION FUNCTIONS ON C ∗ - ALGEBRAS
We prove that the Cuntz semigroup is recovered functorially from the Elliott invariant for a large class of C *-algebras. In particular, our results apply to the largest class of simple C *-algebras for which K-theoretic classification can be hoped for. This work has three significant consequences. First, it provides new conceptual insight into Elliott's classification program, proving that the...
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The Cuntz semigroup of C(X,A) Aaron Tikuisis Doctor of Philosophy Graduate Department of Mathematics University of Toronto 2011
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2014
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2014-05833-9