Inductive limits of semiprojective C⁎-algebras

  title={Inductive limits of semiprojective C⁎-algebras},
  author={Hannes Thiel},
  journal={Advances in Mathematics},
  • Hannes Thiel
  • Published 13 April 2018
  • Mathematics
  • Advances in Mathematics
Rokhlin dimension: duality, tracial properties, and crossed products
We study compact group actions with finite Rokhlin dimension, particularly in relation to crossed products. For example, we characterize the duals of such actions, generalizing previous partial


A characterization of semiprojectivity for subhomogeneous C*-algebras
We study semiprojective, subhomogeneous C*-algebras and give a detailed description of their structure. In particular, we find two characterizations of semiprojectivity for subhomogeneous
Subalgebras of finite codimension in semiprojective C*-algebras
We show that semiprojectivity of a C*-algebra is preserved when passing to C*-subalgebras of finite codimension. In particular, any pullback of two semiprojective C*-algebras over a
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,
Noncommutative semialgebraic sets and associated lifting problems
We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a
Semiprojectivity for Kirchberg algebras
We show that a Kirchberg algebra is semiprojective if and only if it is KK-semiprojective. In particular, this shows that a Kirchberg algebra in the UCT-class is semiprojective if and only if its
On the asymptotic homotopy type of inductive limitC*-algebras
Let X, Y be compact, connected, metrisable spaces with base points Xo, Yo and let denote the compact operators. It is shown that Co(X\xo)| is asymptotically homotopic (or shape equivalent) to
In this paper we relate two topological invariants of a separable C*-algebras. The first is the shape invariant first studied by Effros and Kaminker [EK] and then developed further by Blackadar [B].
Equivalence of the C*-Algebras qℂ and C0(ℝ2) in the Asymptotic Category
The results of Kasparov, Connes, Higson, and Loring imply the coincidence of the functors [[qℂ ⊗ K, B ⊗ K]] = [[C0(ℝ2) ⊗ K, B ⊗ K]] for any C*-algebra B; here[[A, B]] denotes the set of homotopy
Classification of Nuclear, Simple C*-algebras
The possibility that nuclear (or amenable) C*-algebras should be classified up to isomorphism by their K-theory and related invariants was raised in an article by Elliott [48] (written in 1989) in