Just-infinite C∗-algebras and Their Invariants

Mikael Rørdam

doi:10.1093/imrn/rnx227

Just-infinite C^∗-algebras and Their Invariants

Mikael Rørdam^*

^*Corresponding author af dette arbejde

Institut for Matematiske Fag

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.

Originalsprog	Engelsk
Tidsskrift	International Mathematics Research Notices
Vol/bind	2019
Udgave nummer	12
Sider (fra-til)	3621-3645
Antal sider	25
ISSN	1073-7928
DOI	https://doi.org/10.1093/imrn/rnx227
Status	Udgivet - 18 jun. 2019

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10.1093/imrn/rnx227

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Citationsformater

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