Classifiable C*-algebras from minimal Z-actions and their orbit-breaking subalgebras

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00581948" target="_blank" >RIV/67985840:_____/24:00581948 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/s00208-022-02526-1" target="_blank" >https://doi.org/10.1007/s00208-022-02526-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00208-022-02526-1" target="_blank" >10.1007/s00208-022-02526-1</a>

Result language

angličtina

Original language name

Classifiable C*-algebras from minimal Z-actions and their orbit-breaking subalgebras

Original language description

In this paper we consider the question of what abelian groups can arise as the K-theory of C*-algebras arising from minimal dynamical systems. We completely characterize the K-theory of the crossed product of a space X with finitely generated K-theory by an action of the integers and show that crossed products by a minimal homeomorphisms exhaust the range of these possible K-theories. Moreover, we may arrange that the minimal systems involved are uniquely ergodic, so that their C*-algebras are classified by their Elliott invariants. We also investigate the K-theory and the Elliott invariants of orbit-breaking algebras. We show that given arbitrary countable abelian groups G and G1 and any Choquet simplex Δ with finitely many extreme points, we can find a minimal orbit-breaking relation such that the associated C*-algebra has K-theory given by this pair of groups and tracial state space affinely homeomorphic to Δ. We also improve on the second author’s previous results by using our orbit-breaking construction to C*-algebras of minimal amenable equivalence relations with real rank zero that allow torsion in both K and K1. These results have important applications to the Elliott classification program for C*-algebras. In particular, we make a step towards determining the range of the Elliott invariant of the C*-algebras associated to étale equivalence relations.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GJ20-17488Y" target="_blank" >GJ20-17488Y: Applications of C*-algebra classification: dynamics, geometry, and their quantum analogues</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematische Annalen

ISSN

0025-5831

e-ISSN

1432-1807

Volume of the periodical

388

Issue of the periodical within the volume

1

Country of publishing house

DE - GERMANY

Number of pages

27

Pages from-to

703-729

UT code for WoS article

000894571200001

EID of the result in the Scopus database

2-s2.0-85143395812