On topologically zero-dimensional morphisms. (English) Zbl 07823141
Summary: We investigate \(^\ast\)-homomorphisms with nuclear dimension equal to zero. In the framework of classification of \(^\ast\)-homomorphisms, we characterise such maps as those that can be approximately factorised through an AF-algebra.
Along the way, we obtain various obstructions for the total invariant of zero-dimensional morphisms and show that in the presence of real rank zero, nuclear dimension zero can be completely determined at the level of the total invariant. We end by characterising when unital embeddings of \(\mathcal{Z}\) have nuclear dimension equal to zero.
Along the way, we obtain various obstructions for the total invariant of zero-dimensional morphisms and show that in the presence of real rank zero, nuclear dimension zero can be completely determined at the level of the total invariant. We end by characterising when unital embeddings of \(\mathcal{Z}\) have nuclear dimension equal to zero.
MSC:
| 46L35 | Classifications of \(C^*\)-algebras |
| 46L80 | \(K\)-theory and operator algebras (including cyclic theory) |
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