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arXiv · 1703.04562

Convex subquivers and the finitistic dimension

Edward L. Green·Eduardo do N. Marcos
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Abstract

Let $\cQ$ be a quiver and $K$ a field. We study the interrelationship of homological properties of algebras associated to convex subquivers of $\cQ$ and quotients of the path algebra $K\cQ$. We introduce the homological heart of $\cQ$ which is a particularly nice convex subquiver of $\cQ$. For any algebra of the form $K\cQ/I$, the algebra associated to $K\cQ/I$ 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.

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BibTeXRIS

Edward L. Green, Eduardo do N. Marcos. 2017-03-14. Convex subquivers and the finitistic dimension. https://arxiv.org/abs/1703.04562

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