C*-algebras associated to homeomorphisms twisted by vector bundles over finite dimensional spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00582707" target="_blank" >RIV/67985840:_____/24:00582707 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21240/24:00372448

Výsledek na webu

<a href="https://doi.org/10.1090/tran/8900" target="_blank" >https://doi.org/10.1090/tran/8900</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/tran/8900" target="_blank" >10.1090/tran/8900</a>

Jazyk výsledku

angličtina

Název v původním jazyce

C*-algebras associated to homeomorphisms twisted by vector bundles over finite dimensional spaces

Popis výsledku v původním jazyce

In this paper we study Cuntz-Pimsner algebras associated to C*-correspondences over commutative C*-algebras from the point of view of the C*-algebra classification programme. We show that when the correspondence comes from an aperiodic homeomorphism of a finite dimensional infinite compact metric space X twisted by a vector bundle, the resulting Cuntz- Pimsner algebras have finite nuclear dimension. When the homeomorphism is minimal, this entails classification of these C*-algebras by the Elliott invariant. This establishes a dichotomy: when the vector bundle has rank one, the Cuntz-Pimsner algebra has stable rank one. Otherwise, it is purely infinite. For a Cuntz-Pimsner algebra of a minimal homeomorphism of an infinite compact metric space X twisted by a line bundle over X, we introduce orbit breaking subalgebras. With no assumptions on the dimension of X, we show that they are centrally large subalgebras and hence simple and stably finite. When the dimension of X is finite, they are furthermore Z-stable and hence classified by the Elliott invariant.

Název v anglickém jazyce

C*-algebras associated to homeomorphisms twisted by vector bundles over finite dimensional spaces

Popis výsledku anglicky

In this paper we study Cuntz-Pimsner algebras associated to C*-correspondences over commutative C*-algebras from the point of view of the C*-algebra classification programme. We show that when the correspondence comes from an aperiodic homeomorphism of a finite dimensional infinite compact metric space X twisted by a vector bundle, the resulting Cuntz- Pimsner algebras have finite nuclear dimension. When the homeomorphism is minimal, this entails classification of these C*-algebras by the Elliott invariant. This establishes a dichotomy: when the vector bundle has rank one, the Cuntz-Pimsner algebra has stable rank one. Otherwise, it is purely infinite. For a Cuntz-Pimsner algebra of a minimal homeomorphism of an infinite compact metric space X twisted by a line bundle over X, we introduce orbit breaking subalgebras. With no assumptions on the dimension of X, we show that they are centrally large subalgebras and hence simple and stably finite. When the dimension of X is finite, they are furthermore Z-stable and hence classified by the Elliott invariant.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

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

American Mathematical Society. Transactions

ISSN

0002-9947

e-ISSN

1088-6850

Svazek periodika

377

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

44

Strana od-do

1597-1640

Kód UT WoS článku

001150330300001

EID výsledku v databázi Scopus

2-s2.0-85185603548