Colored isomorphism of classifiable C-algebras

Abstract

It is shown that the coloured isomorphism class of a unital, simple, Z-stable, separable amenable C * -algebra satisfying the Universal Coefficient Theorem (UCT) is determined by its tracial simplex. n k=1 u k ψϕ(a)u * k = a and n k=1 v k ϕψ(b)v * k = b for all a ∈ A and all b ∈ B.The present notion, coloured isomorphism, on the other hand, has order zero maps at the level of ultrapowers A ω and B ω (and so includes the case that the ultrapower maps are induced by a sequence of order zero maps at the level

The Cuntz semigroup of unital commutative AI-algebras

“…As a consequence of Lemma 4.18, we will have that Lsc(X, N) is a Cu-semigroup whenever X is a compact metric space (see Corollary 4.19). Recently, this result has been further generalized by Elliott and Im (see [12,Proposition 1.16]).…”

Random amenable C*-algebras

“…The introduction of boundary conditions at the endpoints of the interval (obtaining what are variously referred to as point-line algebras, Elliott-Thomsen building blocks or onedimensional noncommutative CW complexes) provides access to a wider range for the Ktheory of the limit algebra. (To exhaust the full range, in particular to account for torsion in K 0 , one must allow for slightly higher dimensional base spaces; see [16].) That said, our interest in this section is altogether to rid ourselves of this turbulent K-theory, and focus on a class for which the only thing that matters is traces, namely, C * -algebras built from prime dimension drop algebras…”