Document Zbl 0751.46043 - zbMATH Open
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The K-theory of Abelian subalgebras of AF-algebras. (English) Zbl 0751.46043
Summary: Embeddings of commutative \(C^*\)-algebras \(C(X)\) into \(AF\) algebras are constructed when \(X\) has the homotopy type of a finite \(CW\)-complex. The induced maps on \(K_ 0\) are rational isomorphisms. A corollary is that the simple \(AF\) algebra with dimension group \(\mathbb{Z}[1/2]\oplus\mathbb{Z}\) contains MASAs with nontrivial Čech cohomology in any nonzero, even degree. We give new examples of almost commuting matrices and quasi- representations.
MSC:
| 46L80 | \(K\)-theory and operator algebras (including cyclic theory) |