Classification of simple \(C^*\)-algebras: Inductive limits of matrix algebras over one-dimensional spaces
The aim of this paper is the classification of simple \(C^*\)-algebras which can be written as inductive limits of algebras of the form \(A_{n} = \bigoplus_{i=1}^{K_{n}} M_{[n,i]} (C(X_{n,i}))\), where \(X_{n,i}\) is an arbitrary one-dimensional compact metrizable space. This result continues with the classification of simple \(C^*\)-algebras started by \textit{G. Elliott}. The author generalizes previously known results for the case \(X_{n,i}=S^{1}\) and for the case \(X_{n,i}\) being trees and is able to reduce the case of general one-dimensional spaces to circles. The strategies for the proof developed by the author are very technical and of a great interest.
scientific article; zbMATH DE number 1797594
scientific article