Infinitely Many Components in Auslander–Reiten Quivers over Perfect Fields
For a perfect field and a representation-infinite finite-dimensional -algebra , the Auslander–Reiten quiver of has infinitely many connected components. This establishes a conjecture of Auslander, Reiten and Smalø, for finite-dimensional algebras over perfect fields.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Representation Theory of Algebras
- Posed by
- Auslander, Reiten and Smalø
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-27
- Model
- ChatGPT
- Vendor
- OpenAI
- Collaborators
- Wen Chang, Quanyu Tang
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The authors credit ChatGPT with the technical construction and verification of the semilinear twist argument in Lemma 4, and say it was used more substantially in extending the result from algebraically closed fields to arbitrary perfect fields - the step that gives the paper its stated generality.
Verification
No independent review. The disclosure names the specific lemma and the extension the model contributed. Preprint, not refereed.