Non-commutative crepant resolution conjecture for extended Dynkin quivers

Let $Q$ be an extended Dynkin quiver, let $v$ be its extended vertex, and let $\Lambda^1(Q)$ be the multiplicative preprojective algebra at parameter $1$. Let $\delta$ denote the associated dimension vector, let $\mathcal{M}_{1,0}(Q,\delta)$ be the associated multiplicative quiver variety, and let

$$Z(\Lambda^1(Q))\longrightarrow e_v\Lambda^1(Q)e_v, \qquad z\longmapsto e_vz,$$

be the Satake map.

Non-commutative crepant resolution conjecture. The algebra $\Lambda^1(Q)$ is a 2-dimensional non-commutative crepant resolution of its center, the ring of functions on $\mathcal{M}_{1,0}(Q,\delta)$; moreover, the Satake map is an isomorphism.

This is motivated by the analogous structure of ordinary preprojective algebras of extended Dynkin type and by known partial results on the corner algebra $e_v\Lambda^1(Q)e_v$. The conjecture concerns the multiplicative analogue of the du Val-surface and non-commutative-resolution picture.