Just-infinite C-algebras and Their Invariants

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Standard

Just-infinite C-algebras and Their Invariants. / Rørdam, Mikael.

I: International Mathematics Research Notices, Bind 2019, Nr. 12, 2019, s. 3621-3645.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Rørdam, M 2019, 'Just-infinite C-algebras and Their Invariants', International Mathematics Research Notices, bind 2019, nr. 12, s. 3621-3645. https://doi.org/10.1093/imrn/rnx227

APA

Rørdam, M. (2019). Just-infinite C-algebras and Their Invariants. International Mathematics Research Notices, 2019(12), 3621-3645. https://doi.org/10.1093/imrn/rnx227

Vancouver

Rørdam M. Just-infinite C-algebras and Their Invariants. International Mathematics Research Notices. 2019;2019(12):3621-3645. https://doi.org/10.1093/imrn/rnx227

Author

Rørdam, Mikael. / Just-infinite C-algebras and Their Invariants. I: International Mathematics Research Notices. 2019 ; Bind 2019, Nr. 12. s. 3621-3645.

Bibtex

@article{8626a8a448eb4d38bcc96b44ccb9c997,
title = "Just-infinite C∗-algebras and Their Invariants",
abstract = "Just-infinite C∗-algebras, that is, infinite dimensional C∗-algebras, whose proper quotients are finite dimensional, were investigated in [3]. One particular example of a just-infinite residually finite dimensional AF-algebras was constructed in [3]. In this article, we extend that construction by showing that each infinite dimensional metrizable Choquet simplex is affinely homeomorphic to the trace simplex of a just-infinite residually finite dimensional C∗-algebra. The trace simplex of any unital residually finite dimensional C∗-algebra is hence realized by a just-infinite one. We determine the trace simplex of the particular residually finite dimensional AF-algebras constructed in [3], and we show that it has precisely one extremal trace of type II1. We give a complete description of the Bratteli diagrams corresponding to residually finite dimensional AF-algebras. We show that a modification of any such Bratteli diagram, similar to the modification that makes an arbitrary Bratteli diagram simple, will yield a just-infinite residually finite dimensional AF-algebra.",
author = "Mikael R{\o}rdam",
year = "2019",
doi = "10.1093/imrn/rnx227",
language = "English",
volume = "2019",
pages = "3621--3645",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "12",

}

RIS

TY - JOUR

T1 - Just-infinite C∗-algebras and Their Invariants

AU - Rørdam, Mikael

PY - 2019

Y1 - 2019

N2 - Just-infinite C∗-algebras, that is, infinite dimensional C∗-algebras, whose proper quotients are finite dimensional, were investigated in [3]. One particular example of a just-infinite residually finite dimensional AF-algebras was constructed in [3]. In this article, we extend that construction by showing that each infinite dimensional metrizable Choquet simplex is affinely homeomorphic to the trace simplex of a just-infinite residually finite dimensional C∗-algebra. The trace simplex of any unital residually finite dimensional C∗-algebra is hence realized by a just-infinite one. We determine the trace simplex of the particular residually finite dimensional AF-algebras constructed in [3], and we show that it has precisely one extremal trace of type II1. We give a complete description of the Bratteli diagrams corresponding to residually finite dimensional AF-algebras. We show that a modification of any such Bratteli diagram, similar to the modification that makes an arbitrary Bratteli diagram simple, will yield a just-infinite residually finite dimensional AF-algebra.

AB - Just-infinite C∗-algebras, that is, infinite dimensional C∗-algebras, whose proper quotients are finite dimensional, were investigated in [3]. One particular example of a just-infinite residually finite dimensional AF-algebras was constructed in [3]. In this article, we extend that construction by showing that each infinite dimensional metrizable Choquet simplex is affinely homeomorphic to the trace simplex of a just-infinite residually finite dimensional C∗-algebra. The trace simplex of any unital residually finite dimensional C∗-algebra is hence realized by a just-infinite one. We determine the trace simplex of the particular residually finite dimensional AF-algebras constructed in [3], and we show that it has precisely one extremal trace of type II1. We give a complete description of the Bratteli diagrams corresponding to residually finite dimensional AF-algebras. We show that a modification of any such Bratteli diagram, similar to the modification that makes an arbitrary Bratteli diagram simple, will yield a just-infinite residually finite dimensional AF-algebra.

UR - http://www.scopus.com/inward/record.url?scp=85072080615&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnx227

DO - 10.1093/imrn/rnx227

M3 - Journal article

AN - SCOPUS:85072080615

VL - 2019

SP - 3621

EP - 3645

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 12

ER -

ID: 230391787