Geodesic
The generator rank of subhomogeneous $C^*\!$-algebras
Canadian journal of mathematics, Tome 75 (2023) no. 4, pp. 1314-1342

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DOI

We compute the generator rank of a subhomogeneous $C^*\!$-algebra in terms of the covering dimension of the pieces of its primitive ideal space corresponding to irreducible representations of a fixed dimension. We deduce that every $\mathcal {Z}$-stable approximately subhomogeneous algebra has generator rank one, which means that a generic element in such an algebra is a generator.This leads to a strong solution of the generator problem for classifiable, simple, nuclear $C^*\!$-algebras: a generic element in each such algebra is a generator. Examples of Villadsen show that this is not the case for all separable, simple, nuclear $C^*\!$-algebras.
DOI : 10.4153/S0008414X22000268
Mots-clés : C*-algebras, generator rank, generator problem, single generation 
Thiel, Hannes. The generator rank of subhomogeneous $C^*\!$-algebras. Canadian journal of mathematics, Tome 75 (2023) no. 4, pp. 1314-1342. doi: 10.4153/S0008414X22000268
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     title = {The generator rank of subhomogeneous $C^*\!$-algebras},
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     year = {2023},
     volume = {75},
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     doi = {10.4153/S0008414X22000268},
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