Decomposition Rank of Subhomogeneous C*‐Algebras

By W. Winter. 2002

56 citations recorded by the source corpus.

We analyze the decomposition rank (a notion of covering dimension for nuclear C*‐algebras introduced by E. Kirchberg and the author) of subhomogeneous C*‐algebras. In particular, we show that a subhomogeneous C*‐algebra has decomposition rank n if and only if it is recursive subhomogeneous of topological dimension n, and that n is determined by the primitive ideal space.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4ac87df98cfd5e5f9ac5152542ab00c9c50041cf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. W. Winter
2. Stuart White
3. Aaron Tikuisis
4. Andrew S. Toms
5. G'abor Szab'o
6. Eberhard Kirchberg
7. M. Rørdam
8. Yasuhiko Sato

In Computational Theory and Mathematics

1. Andrew S. Toms
2. Aaron Tikuisis
3. Eberhard Kirchberg
4. Stuart White
5. W. Winter

In Mathematical Physics

1. W. Winter
2. Stuart White
3. Aaron Tikuisis
4. G'abor Szab'o
5. Andrew S. Toms
6. David Kerr
7. Eberhard Kirchberg
8. Yasuhiko Sato

Citations in the corpus

• FLAT DIMENSION GROWTH FOR C ∗ -ALGEBRAS (2005, background): “Let dr(•) denote the decomposition rank of a nuclear C ∗-algebra. In [ 39 ] it is proved that”
• Quasidiagonality of nuclear C*-algebras (2015, background): “ models constructed in [29] (since those exhaust the invariant), which in turn have topological dimension at most 2, as pointed out in [78, 1.11]; the UCT is of course necessary for this argument. By [78] these models have decomposition rank at most 2, and therefore so does the limit Aby [46, (3.2)]”
• Strongly self-absorbing C*-algebras (2005, methodology): “We refer the interested reader to [29], [28] and [41] for more details on recursive subhomogeneous C∗-algebras.”
• COVERING DIMENSION AND QUASIDIAGONALITY (2002, background): “(iii) In [24] it will be shown that, for a subhomogeneous algebra A, we have drA = maxk dim(PrimkA), where PrimkA is the (locally compact Hausdorff) space of kernels of k-dimensional irreducible representations.”
• Minimal Dynamics and K-Theoretic Rigidity: Elliott’s Conjecture (2009, methodology): “It then follows from the main theorem of [ 29 ] that each AYm has decomposition rank at most dim(X).”