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arXiv · 1407.2672

Truncated path algebras are homologically transparent

A. Dugas·B. Huisgen-Zimmermann·J. Learned
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Abstract

It is shown that path algebras modulo relations of the form $\Lambda = KQ/I$, where $Q$ is a quiver, $K$ a coefficient field, and $I \subseteq KQ$ the ideal generated by all paths of a given length, can be readily analyzed homologically, while displaying a wealth of phenomena. In particular, the syzygies of their modules, and hence their finitistic dimensions, allow for smooth descriptions in terms of $Q$ and the Loewy length of $\Lambda$. The same is true for the distributions of projective dimensions attained on the irreducible components of the standard parametrizing varieties for the modules of fixed $K$- dimension.

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A. Dugas, B. Huisgen-Zimmermann, J. Learned. 2014-07-10. Truncated path algebras are homologically transparent. https://arxiv.org/abs/1407.2672

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