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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.

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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

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VibeMathed
registry · event recorded by

Wen Chang
human · human collaborator

Quanyu Tang
human · human collaborator

ChatGPT
model · ai model contributor · OpenAI

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This event attributed to Quanyu Tang

This event attributed to Wen Chang

This event attributed to ChatGPT

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Infinitely Many Components in Auslander–Reiten Quivers over Perfect Fields — Mathematical Frontier Network