2017/05/08 by Mikael Rørdam, Mikael Rordam, Rordam, Mikael
Mathematics · #46L05 #46L35 #46L45 #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L05 #msc:46L35 #msc:46L45
paper · pdf · doi:10.48550/arxiv.1705.02818
22 pages. A more detailed proof of Proposition 2.2 is included in this version, and a missing condition in Proposition 2.2 (and Corollary 2.3) is added. To appear in Int. Math. Res. Not. IMRN
openalex publication_date 2017/05/08 · arxiv created 2017/12/28 · arxiv updated 2017/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Just-infinite C*-algebras, i.e., infinite dimensional C*-algebras, whose proper quotients are finite dimensional, were investigated in [Grigorchuk-Musat-Rordam, 2016]. One particular example of a just-infinite residually finite dimensional AF-algebras was constructed in that article. 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*-algebras. 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 the above mentioned article, 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.