We study the specializations Lg,nε at roots of unity ε of odd order of the graph algebras, associated to a simply-connected complex semi-simple algebraic group G and a compact oriented surface Σg,n∘
Nearby in the stack
with genus
g
,
n
punctures, and one boundary component. We prove that the central localizations of
Lg,nε
and of its subalgebra
Lg,nuε
of invariant elements under the coadjoint action of a small quantum group, are central simple algebras of PI degrees that we compute. Also, we describe their centers, and show they are integrally closed rings.