A classification of simple limits of splitting interval algebras
Splitting interval algebras take the form \(\{f\in M_n(C[0,1]):f(0)\in\oplus M_{p_i},\;f(1)\in\oplus M_{q_j}\}\) where the \(\{p_i\}\) and \(\{q_j\}\) each sum to \(n\). The main theorem of the paper classifies simple unital inductive limits of finite direct sums of such algebras in terms of scaled ordered groups and tracial state spaces. This fits into \textit{G. Elliott}'s classification program for amenable \(C^*\)-algebras as surveyed in [Proceedings of the international congress of mathematicians, ICM '94, August 3-11, 1994, Zürich, Switzerland. Vol. II. Basel: Birkhäuser, 922-932 (1995)].
simple limits of splitting interval algebras
scientific article; zbMATH DE number 1106589
scientific article