Abstract
AbstractWe prove that if the Auslander–Reiten triangles generate the relations for the Grothendieck group of a Hom-finite Krull–Schmidt triangulated category with a (co)generator, then the category has only finitely many isomorphism classes of indecomposable objects up to translation. This gives a triangulated converse to a theorem of Butler and Auslander–Reiten on the relations for Grothendieck groups. Our approach has applications in the context of Frobenius categories.
Funder
NTNU Norwegian University of Science and Technology
Publisher
Springer Science and Business Media LLC
Cited by
1 articles.
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