Quasidiagonality of nuclear \(\mathrm{C}^\ast\)-algebras
The main result of the paper is the following remarkable theorem: Let \(A\) be a separable nuclear \(C^*\)-algebra that satisfies the UCT. Then every faithful trace on \(A\) is quasidiagonal. This result has several important corollaries. Here are some of them: {\parindent=0.6cm \begin{itemize}\item[(1)] Every separable nuclear \(C^*\)-algebra with a faithful trace that satisfies the UCT is quasidiagonal. \item[(2)] The reduced group \(C^*\)-algebras of discrete amenable groups is quasidiagonal (this answers the Rosenberg conjecture). \item[(3)] Separable unital simple infinite-dimensional \(C^*\)-algebras of finite nuclear dimension that satisfy the UCT are classified by the Elliott invariant. \end{itemize}}
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