A note on homological properties of Nakayama algebras
Dawei Shen
TL;DR
This paper introduces a quick algorithm based on the resolution quiver to determine if a connected Nakayama algebra has finite global dimension and is Gorenstein, enhancing previous results by Ringel.
Contribution
It provides a fast algorithm for assessing homological properties of Nakayama algebras using the resolution quiver, improving efficiency over prior methods.
Findings
Algorithm efficiently determines finite global dimension.
Algorithm assesses Gorenstein property.
Strengthens Ringel's previous results.
Abstract
Using the resolution quiver for a connected Nakayama algebra, a fast algorithm is given to decide whether its global dimension is finite or not and whether it is Gorenstein or not. The latter strengthens a result of Ringel.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology