Abstract
Let Q be a finite quiver without oriented cycles. Denote by U → ℳ(Q) the fine moduli space of stable thin sincere representations of Q with respect to the canonical stability notion. We prove Extℳ(Q)l (U, U) = 0 for all l > 0 and compute the endomorphism algebra of the universal bundle U. Moreover, we obtain a necessary and sufficient condition for when this algebra is isomorphic to the path algebra of the quiver Q. If so, then the bounded derived categories of finitely generated right k Q-modules and that of coherent sheaves on ℳ(Q) are related via the full and faithful functor − ⊗kQL U.
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