Crossed Products of the Cantor Set by Free Minimal Actions of ℤd
By N. Christopher Phillips. 2002
68 citations recorded by the source corpus.
Let d be a positive integer, let X be the Cantor set, and let ℤd act freely and minimally on X. We prove that the crossed product C*(ℤd,X) has stable rank one, real rank zero, and cancellation of projections, and that the order on K0(C*(ℤd,X)) is determined by traces. We obtain the same conclusion for the C*-algebras of various kinds of aperiodic tilings.
Subfields: Materials Chemistry, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a35d4a19d2761011faf9b14ae8b1a298710103b3
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In Materials Chemistry
In Mathematical Physics
- Aidan Sims
- Efren Ruiz
- Toke Meier Carlsen
- Hiroyuki Osaka
- N. Christopher Phillips
- M. Tomforde
- Christopher Phillips
- Trent Yeend
Citations in the corpus
- Stable and real rank for crossed products by automorphisms with the tracial Rokhlin property (2004, methodology): “ of C∗(Z,A,α) which are stably isomorphic to A.The next three sections treat, in order, the order on projections, real rank zero, and stable rank one. These are the analogs of Sections 3, 4, and 5 of [27]. It is in Section 4 that the weaker conditions satisfied by the subalgebras cause the greatest a”
- Reconstruction of groupoids and C*-rigidity of dynamical systems (2017, background): “9 of [35] shows that ι extends to an injective homomorphism from C r (c (e)) to C r (G).”
- Large subalgebras (2014, background): “Large subalgebras (without the name) play a key role in [27], where they are used to prove that if Z acts freely and minimally on the Cantor set X , then C(Z, X) has real rank zero, stable rank one, and order on projections determined by traces.”