6 problems

Let $A$ be a simple, stably finite, nuclear C-algebra. Elliott's conjecture. The algebra $A$ should be quasidiagonal. This is stated as a consequence predicted by Elliott's classif…

Elliott's trace approximation conjecture. Every trace on $A$ has that strongest approximation property:

Let $A$ be a separable exact quasidiagonal $C^*$-algebra. AF-embedding conjecture. $A$ is isomorphic to a subalgebra of an AF algebra. The preceding theorem gives strong evidence f…

A strongly self-absorbing $c*$-algebra is a separable $c*$-algebra $a9$ for which there is an approximately unitarily equivalent isomorphism $a9\cong a9\otimesa9$. A $c*$-algebra i…

Let $G$ be an amenable countable discrete group, and let $C^*_r(G)$ denote its reduced group $C^*$-algebra. Quasidiagonality conjecture. The algebra $C^*_r(G)$ is quasidiagonal. Th…

Let $G$ be a countable amenable group, and let $C_r^*(G)$ denote its reduced $C^*$-algebra. Quasidiagonality conjecture. The reduced $C^*$-algebra $C_r^*(G)$ is quasidiagonal. This…