2026-04-18T03:39:36Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/3775512024-12-20T14:13:30Zcom_2072_199267com_2072_4427col_2072_199862

2020-10-14T11:48:07Z urn:hdl:2072/377551 Just-infinite $ C^*$ -algebras and their invariants Rørdam, M. 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. 2020-10-14T11:48:07Z 2024-09-19T13:27:24Z 2020-10-14T11:48:07Z 2024-09-19T13:27:24Z 2017-01-01 info:eu-repo/semantics/preprint http://hdl.handle.net/2072/377551 eng CRM Preprints info:eu-repo/semantics/openAccess L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons:http://creativecommons.org/licenses/by-nc-nd/4.0/ RECERCAT (Dipòsit de la Recerca de Catalunya)