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Classification of Certain Simple C*-Algebras with Torsion in K1

Published online by Cambridge University Press:  20 November 2018

Jesper Mygind*
Affiliation:
The Fields Institute, 222 College Street, Toronto, Ontario, M5T 3J1. email: jmygind@hotmail.com
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Abstract

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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.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2001

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