8 problems

Talented monoid classification conjecture. The following are equivalent: $T_E$ and $T_F$ are $\mathbb Z$-isomorphic; $L_\mathsf{k}(E)$ and $L_\mathsf{k}(F)$ are graded Morita equiv…

Equivariant classification conjecture. There is an order-preserving $\mathbb Z[x,x^{-1}]$-module isomorphism

Let a graph $C^*$-algebra be equipped with its filtered $K$-theory, consisting of the $K$-theory of certain ideals and quotients together with the associated long exact sequences.…

Graph extension conjecture. The following are equivalent:

Let $E$ and $F$ be directed graphs, and let $L_{\mathbb{C}}(E)$ and $L_{\mathbb{C}}(F)$ be their Leavitt path algebras over the complex numbers, while $C^*(E)$ and $C^*(F)$ are the…

Let $E$ and $F$ be directed graphs, let $L_{\mathbb{C}}(E)$ and $L_{\mathbb{C}}(F)$ be their Leavitt path algebras, and let $C^*(E)$ and $C^*(F)$ be the associated graph $C^*$-alge…

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 $\mathcal{C}$ be the class of graphs $E$ such that $C^*(E)$ has finitely many ideals; equivalently, in the supplied context, such that $L_\mathbb{C}(E)$ has finitely many ideal…