The classification of certain non-simple approximate interval algebras. (English) Zbl 0926.46047
Fillmore, Peter A. (ed.) et al., Operator algebras and their applications II. Selected papers from the seminars and workshops held at The Fields Institute for Research in Mathematical Sciences, Waterloo, ON, Canada, 1994–1995. Providence, RI: American Mathematical Society. Fields Inst. Commun. 20, 105-148 (1998).
Summary: Certain separable, unital, amenable, non-simple \(C^*\)-algebras are classified by establishing that the essential structure of such algebras is encapsulated in the \(K_0\) group of the algebra along with the simplex of tracial states of the algebra cut down by projections
\[
A\cong B\Leftrightarrow \begin{cases} \varphi_0: K_0(A)@>\cong>> K_0(B)\\ T(eAe)@>\cong>> T(\varphi_0(e) B\varphi_0(e))\\ \forall e\in \text{proj}(A)\end{cases}.
\]
For the entire collection see [Zbl 0896.00025].
For the entire collection see [Zbl 0896.00025].
MSC:
| 46L35 | Classifications of \(C^*\)-algebras |
| 46L80 | \(K\)-theory and operator algebras (including cyclic theory) |
