13 problems

AF-embeddability characterization conjecture. A C-algebra is AF embeddable if, and only if, it is separable, exact, and quasidiagonal.

Power's algebraic-isometric isomorphism conjecture. Algebraic isomorphism may be equivalent to isometric isomorphism for subalgebras of AF $C^*$-algebras containing a regular canon…

Let $A_{\theta}$ be an irrational rotation algebra equipped with the relevant action of a finite cyclic subgroup ${\mathbb{Z}}_n$ of $SL_2({\mathbb{Z}})$, for $n\in\{2,3,4,6\}$. Th…

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…

Nine dual spaces conjecture. There are precisely nine isomorphism types of dual Banach spaces arising from Type I AF C-algebras.

Diagonal-filling conjecture. The difference between these cases is due to the diagonal in $\mathcal{B}$ being filled by $\phi$ in the second and fourth cases, while a remaining zer…

Phillips's conjecture. There does not exist a totally $K$-free AF-action of $G$ on $A$.

Let $A$ be a stable simple AF algebra not isomorphic to $\mathbb{K}$. Write $TW(A)$ for the tracial state space associated with $A$, $U_\to(A)$ for the relevant infinite-dimensiona…

Let $A$ be an AF-algebra. A unital quotient of $A$ means a quotient $A/I$ that is unital. AF-algebra graph C-algebra characterization conjecture. $A$ is isomorphic to a graph $C^*$…

Let $\Gamma$ be a countable distributive lattice, realized as the lattice of finite ideals of a partially ordered set, and let $A(\Gamma)$ be the $AF$-algebra associated with the H…

Let $\mathcal Z$ be the Jiang--Su algebra and let … For a graph $G$, let $B(G)$ denote the associated CCR algebra. Non-realizability claim. The algebra $A_{\aleph_0\aleph_1}$ is no…

Let $E_{CM}$ be an elliptic curve with complex multiplication, and let $G_A$ be its associated $AF$-algebra. For each prime $p$, let $L_p$ be the integer matrix … and let…

Let $E_{CM}\cong E(K)$ be an elliptic curve with complex multiplication. Let $E_{tors}(K)$ be the finite-order subgroup of $E(K)$. If $K'\supset K$ is a non-trivial extension obtai…