CONVEX SUBQUIVERS AND THE FINITISTIC DIMENSION

摘要

Let Q be a quiver and K a field. We study the interrelationship of homological properties of algebras associated to convex subquivers of Q and quotients of the path algebra KQ. We introduce the homological heart of Q which is a particularly nice convex subquiver of Q. For any algebra of the form KQ/I, the algebra associated to KQ/I and the homological heart have similar homological properties. We give an application showing that the finitistic dimension conjecture need only be proved for algebras with path connected quivers.