Just-infinite C*-algebras and their invariants
| Autor: | Rordam, Mikael |
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| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 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. Comment: 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 |
| Databáze: | arXiv |
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