## 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 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.

Original language | English |
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Journal | International Mathematics Research Notices |

Volume | 2019 |

Issue number | 12 |

Pages (from-to) | 3621-3645 |

Number of pages | 25 |

ISSN | 1073-7928 |

DOIs | |

Publication status | Published - 2019 |