Classification of Certain Simple C*-Algebras with Torsion in K 1

Mygind, Jesper

Canadian journal of mathematics, Tome 53 (2001) no. 6, pp. 1223-1308

Résumé

We show that the Elliott invariant is a classifying invariant for the class of ${{C}^{*}}$ -algebras that are simple unital infinite dimensional inductive limits of finite direct sums of building blocks of the form $$\left\{ f\in C\left( \mathbb{T} \right)\otimes {{M}_{n}}:f\left( {{x}_{i}} \right)\in {{M}_{{{d}_{i}}}},i=1,2,...,N \right\},$$ where ${{x}_{1}},\,{{x}_{2.}},...,{{x}_{N\,}}\in \mathbb{T},{{d}_{1}},{{d}_{2}},.\,.\,.,{{d}_{N}}$ are integers dividing $n$ , and ${{M}_{{{d}_{i}}}}$ is embedded unitally into ${{M}_{n}}$ . Furthermore we prove existence and uniqueness theorems for $*$ -homomorphisms between such algebras and we identify the range of the invariant.

Détail

DOI : 10.4153/CJM-2001-046-2

Mots-clés : 46L80, 19K14, 46L05

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