3 problems

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 $E$ and $F$ be row-finite graphs over a field $K$. Write $\operatorname{\mathcal L}_K(E)$ and $\operatorname{\mathcal L}_K(F)$ for their Leavitt path algebras, and let…

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…