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Infinitely Many Components in Auslander–Reiten Quivers over Perfect Fields

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auslander-reiten-smalo-perfect-fieldsAlgebraposed by Auslander, Reiten and Smalørecorded: solved

1 attempt · no person has looked

Statement

For a perfect field kk and a representation-infinite finite-dimensional kk-algebra AA, the Auslander–Reiten quiver of AA has infinitely many connected components. This establishes a conjecture of Auslander, Reiten and Smalø, for finite-dimensional algebras over perfect fields.

Context

A named conjecture of Auslander, Reiten and Smalø, established over perfect fields rather than only in special cases.

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  • #1

    Attempt 1

    proof attemptChatGPT with Wen Chang, Quanyu Tang ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    ChatGPT
    people
    Wen Chang, Quanyu Tang

    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.

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