Given a representation-finite (finite dimensional over a field) quiver algebra of finite global dimension. Is $eAe$ isomorphic to the field for at least one primitive idempotent $e$? This is true for Nakayama algebras (and trivially for acyclic algebras).
added (quivers) tag - if it does not fit for some reason, feel free to revert my edit
Martin Sleziak
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