2019/04/04 by Johanne Haugland, Haugland, Johanne
Mathematics · #16G70 (secondary) #18E10 #18E30 #18F30 (primary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1904.02506
openalex publication_date 2019/04/04 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
We prove that if the Auslander-Reiten triangles generate the relations for\nthe Grothendieck group of a Hom-finite Krull-Schmidt triangulated category with\na (co)generator, then the category has only finitely many isomorphism classes\nof indecomposable objects up to translation. This gives a triangulated converse\nto a theorem of Butler and Auslander-Reiten on the relations for Grothendieck\ngroups. Our approach has applications in the context of Frobenius categories.\n