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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ20-17488Y" target="_blank" >GJ20-17488Y: Aplikace klasifikace C*-algeber: dynamika, geometrie a jejich kvantové analogie</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Mathematische Annalen

ISSN

0025-5831

e-ISSN

1432-1807

Svazek periodika

388

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

27

Strana od-do

703-729

Kód UT WoS článku

000894571200001

EID výsledku v databázi Scopus

2-s2.0-85143395812