The generator rank of C⁎-algebras

@article{Thiel2012TheGR,
  title={The generator rank of C⁎-algebras},
  author={Hannes Thiel},
  journal={arXiv: Operator Algebras},
  year={2012}
}
  • Hannes Thiel
  • Published 24 October 2012
  • Mathematics
  • arXiv: Operator Algebras
View PDF on arXiv
4 Citations
Background Citations
2

4 Citations

The generator rank of subhomogeneous C*-algebras
We compute the generator rank of a subhomgeneous C*-algebra in terms of the covering dimension of the pieces of its primitive ideal space corresponding to irreducible representations of a fixed…
Games on AF-algebras
. We analyze C ∗ -algebras, particularly AF-algebras, and their K 0 -groups in the context of the infinitary logic L ω 1 ω . Given two separable unital AF-algebras A and B , and considering their K 0…
Generators in $\mathcal{Z}$-stable C*-algebras of real rank zero.
We show that every separable C*-algebra of real rank zero that tensorially absorbs the Jiang-Su algebra contains a dense set of generators. It follows that in every classifiable, simple, nuclear…
Large Irredundant Sets in Operator Algebras
Abstract A subset ${\mathcal{X}}$ of a C*-algebra ${\mathcal{A}}$ is called irredundant if no $A\in {\mathcal{X}}$ belongs to the C*-subalgebra of ${\mathcal{A}}$ generated by ${\mathcal{X}}\setminus…

References

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In topological K-theory, which can be viewed as the algebraic side of the theory of vector bundles, some of the interesting properties which one investigates are, for example, the conditions under…
Inductive limits of projective $C$*-algebras
  • Hannes Thiel
  • Mathematics
    Journal of Noncommutative Geometry
  • 2020
We show that a separable C*-algebra is an inductive limits of projective C*-algebras if and only if it has trivial shape, that is, if it is shape equivalent to the zero C*-algebra. In particular,…
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The generator problem for Z-stable C*-algebras
The generator problem was posed by Kadison in 1967, and it remains open until today. We provide a solution for the class of C*-algebras absorbing the Jiang-Su algebra Z tensorially. More precisely,…
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We mainly treat a separable C*-algebra A in this article. Let S be a subset of Asa. We call S a generator of A when any C*-subalgebra B of A containing S is equal to A, and we denote A = C∗(S). If S…
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GENERATORS AND DIRECT INTEGRAL DECOMPOSITIONS OF {W^ * }-ALGEBRAS
Let A be a W*-algebra on separable Hubert space H. A is singly generated if there is an operator TeA such that A is the smallest W*algebra containing T. It has long been conjectured that every A is…
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