Universal AF-algebras
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Universal AF-algebras
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Functional Analysis
ISSN
0022-1236
e-ISSN
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Volume of the periodical
279
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
32
Pages from-to
108590
UT code for WoS article
000532828700007
EID of the result in the Scopus database
2-s2.0-85083368661