Universal AF-algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00524482" target="_blank" >RIV/67985840:_____/20:00524482 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jfa.2020.108590" target="_blank" >https://doi.org/10.1016/j.jfa.2020.108590</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jfa.2020.108590" target="_blank" >10.1016/j.jfa.2020.108590</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Universal AF-algebras

Popis výsledku v původním jazyce

We study the approximately finite-dimensional (AF) C⁎-algebras that appear as inductive limits of sequences of finite-dimensional C⁎-algebras and left-invertible embeddings. We show that there is such a separable AF-algebra AF which is a split-extension of any finite-dimensional C⁎-algebra and has the property that any separable AF-algebra is isomorphic to a quotient of AF. Equivalently, by Elliott's classification of separable AF-algebras, there are surjectively universal countable scaled (or with order-unit) dimension groups. This universality is a consequence of our result stating that AF is the Fraïssé limit of the category of all finite-dimensional C⁎-algebras and left-invertible embeddings. With the help of Fraïssé theory we describe the Bratteli diagram of AF and provide conditions characterizing it up to isomorphisms. AF belongs to a class of separable AF-algebras which are all Fraïssé limits of suitable categories of finite-dimensional C⁎-algebras, and resemble C(2N) in many senses. For instance, they have no minimal projections, tensorially absorb C(2N) (i.e. they are C(2N)-stable) and satisfy similar homogeneity and universality properties as the Cantor set.

Název v anglickém jazyce

Universal AF-algebras

Popis výsledku anglicky

We study the approximately finite-dimensional (AF) C⁎-algebras that appear as inductive limits of sequences of finite-dimensional C⁎-algebras and left-invertible embeddings. We show that there is such a separable AF-algebra AF which is a split-extension of any finite-dimensional C⁎-algebra and has the property that any separable AF-algebra is isomorphic to a quotient of AF. Equivalently, by Elliott's classification of separable AF-algebras, there are surjectively universal countable scaled (or with order-unit) dimension groups. This universality is a consequence of our result stating that AF is the Fraïssé limit of the category of all finite-dimensional C⁎-algebras and left-invertible embeddings. With the help of Fraïssé theory we describe the Bratteli diagram of AF and provide conditions characterizing it up to isomorphisms. AF belongs to a class of separable AF-algebras which are all Fraïssé limits of suitable categories of finite-dimensional C⁎-algebras, and resemble C(2N) in many senses. For instance, they have no minimal projections, tensorially absorb C(2N) (i.e. they are C(2N)-stable) and satisfy similar homogeneity and universality properties as the Cantor set.

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

2020

Kód důvěrnosti údajů

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

Název periodika

Journal of Functional Analysis

ISSN

0022-1236

e-ISSN

—

Svazek periodika

279

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

32

Strana od-do

108590

Kód UT WoS článku

000532828700007

EID výsledku v databázi Scopus

2-s2.0-85083368661