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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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algebraJul 27, 2026Significance 20/100Registry: unreviewed

Infinitely Many Components in Auslander–Reiten Quivers over Perfect Fields

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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.

Source authenticatedInfinitely Many Components in Auslander–Reiten Quivers over Perfect Fields →
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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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