Infinitely Many Components in Auslander–Reiten Quivers over Perfect Fields
For a perfect field $k$ and a representation-infinite finite-dimensional $k$-algebra $A$, the Auslander–Reiten quiver of $A$ has infinitely many connected components. This establishes a conjecture of Auslander, Reiten and Smalø, for finite-dimensional algebras over perfect fields.
Exact FrontierDelta
Scope and record
Occurred: Jul 27, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: Infinitely Many Components in Auslander–Reiten Quivers over Perfect Fields · Auslander–Reiten–Smalø
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Wen Chang
human · human collaborator
Quanyu Tang
human · human collaborator
ChatGPT
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Quanyu Tang
This event attributed to Wen Chang
This event attributed to ChatGPT