Just-infinite C∗-algebras and Their Invariants
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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 tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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