9 problems

Let $E$ and $F$ be finite graphs, let $\mathsf{k}$ be a field, and write $L_{\mathsf{k}}(E)$ and $L_{\mathsf{k}}(F)$ for their Leavitt path algebras. Their graded Grothendieck grou…

Let $E$ and $F$ be finite graphs, and let $K$ be a field. For a … -graded case with its natural $\mathbb{Z}[x,x^{-1}]$-module structure. Let $T_E$ denote the talented monoid of $E$…

Hazrat's fullness conjecture. There exists a unital $\mathbb{Z}$-graded $\mathsf{k}$-homomorphism $\psi:L(E)\rightarrow L(F)$ such that

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

Let $\ell$ be a field. Consider the category of unital Leavitt path $\ell$-algebras with graded homomorphisms modulo inner automorphisms, and the category of preordered abelian gro…

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…

Let $E_1$ and $E_2$ be finite graphs and $F$ a field. Write $M^{\operatorname{gr}}_{E_i}$ for the graded graph monoid and $K_0^{\operatorname{gr}}(L_F(E_i))$ for the graded Grothen…

Let $K_0^{\operatorname{gr}}$ denote the graded Grothendieck group functor. Consider the category whose objects are Leavitt path algebras and whose morphisms are graded homomorphis…

Let $E$ and $F$ be row-finite graphs. Write $\operatorname{\mathcal L}(E)$ and $\operatorname{\mathcal L}(F)$ for their Leavitt path algebras, with graded isomorphisms denoted by…