1. Given a field $K$, is there a finite dimensional quiver algebra, such that any finite dimensional division algebra is isomorphic to End(M)/rad(End(M)) for some indecomposable finite dimensional module M?
 2. Can fields with finite Brauer group be somehow characterised?
 3. What are the field with Brauer group equal to $\mathbb{Z}/\mathbb{Z}3$? I do not even know one example. ($\mathbb{Z}/\mathbb{Z}3$ might be replaced by any finite abelian group with at least 3 elements)