5 problems

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

Let $E$ and $F$ be finite graphs, let $k$ be a field, let $C^*(E)$ and $C^*(F)$ denote their graph $C^*$-algebras, let $L_k(E)$ and $L_k(F)$ denote their Leavitt path algebras, and…

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…