Title: Just-infinite C*-algebras and their invariants,
Abstract: 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.