I have a simple question. If I am not wrong, we can define $\tilde{A}_l$ affine Dynkin quiver of type A, for $l\geq1$. It has $l+1$ vertices that we can order from $0$ to $l$ such that $i$ is connected with $i+1$ and $l$ with $0$.
The Jordan quiver is instead a quiver composed by a single vertex and a loop arrow.
So, it makes sense to think a Jordan quiver as "$\tilde{A}_0$". Is this a standard identification? If not, what are problems with that?
With respect to the normal numbering $\tilde A_n$ is an $(n+1)$-cycle. In particular, yes, it is reasonable to call the Jordan quiver $\tilde A_0$. See for example chapter 4 of Derksen and Weyman's Introduction to quiver representations, where they do use this notation (at least for the graphs, all they are interested in at that point).