2026-04-04T01:27:30Zhttps://recercat.cat/oai/requestoai:recercat.cat:2072/3775512024-12-20T14:13:30Zcom_2072_199267com_2072_4427col_2072_199862
RECERCAT
author
Rørdam, M.
2020-10-14T11:48:07Z2024-09-19T13:27:24Z
2020-10-14T11:48:07Z2024-09-19T13:27:24Z
2017-01-01
http://hdl.handle.net/2072/377551
Just-infinite C* s, i.e., infinite dimensional C* s, whose proper quotients are finite dimensional, were investigated in \cite{GMR:JI}. One particular example of a just-infinite residually finite dimensional AF-algebras was constructed in \cite{GMR:JI}. In this paper 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*. The trace simplex of any unital residually finite dimensional C*{} is hence realized by a just-infinite one. We determine the trace simplex of the particular residually finite dimensional AF-algebras constructed in \cite{GMR:JI}, and we show that it has precisely one extremal trace of type II$ _1$ . 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.
eng
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Just-infinite $ C^*$ -algebras and their invariants
info:eu-repo/semantics/preprint
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https://recercat.cat/bitstream/2072/377551/1/J1-RFD-JI-CRMMaRcAt.pdf
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J1-RFD-JI-CRMMaRcAt.pdf
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https://recercat.cat/bitstream/2072/377551/5/J1-RFD-JI-CRMMaRcAt.pdf.txt
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J1-RFD-JI-CRMMaRcAt.pdf.txt