8 problems

Decomposability conjecture. $A$ is decomposable if and only if $K_1(A)$ is torsion free.

Blackadar's conjecture. $A$ is semiprojective if and only if its $K$-theory is finitely generated.

Let $G_0$ and $G_1$ be countable abelian groups, let $\alpha_i$ be automorphisms of $G_i$ of prime orders $p_i$, and let $H_i\subseteq G_i$ be $\alpha_i$-invariant subgroups satisf…

Matui–Izumi classification conjecture. The transformation

Kirchberg complexity-rank conjecture. Every UCT Kirchberg algebra has complexity rank at most two.

Classification conjecture for unital actions. The following are equivalent:

Classifying-space conjecture. The map

Let $G$ be a countable torsion-free amenable group and let $d4ad4d$ be a strongly self-absorbing $C^*$-algebra. An action of $G$ on $d4ad4d$ is strongly outer when each nontrivial…