Abstract:We classify connected finite acyclic graded quivers $Q$ for which the graded path algebra $kQ$, regarded as a formal dg algebra, is silting-discrete. We prove that $kQ$ is silting-discrete if and only if it is derived-discrete, and that both conditions are equivalent to the underlying graph of $Q$ being of type ADE, or of type $\widetilde{A}$ with unequal clockwise and counter-clockwise total degrees. The key ingredient is an explicit construction of an infinite pre-simple-minded collection in $\\text{pvd } kQ$ in the non-discrete case.
| Comments: | 10 pages |
| Subjects: | Representation Theory (math.RT) |
| MSC classes: | 16E35, 16E45, 16G20, 18G80 |
| Cite as: | arXiv:2605.23704 [math.RT] |
| (or arXiv:2605.23704v1 [math.RT] for this version) | |
| https://doi.org/10.48550/arXiv.2605.23704 arXiv-issued DOI via DataCite (pending registration) |
From: Riku Fushimi [view email]
[v1]
Fri, 22 May 2026 14:53:24 UTC (13 KB)
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