{"paper":{"title":"Bilinear forms on Grothendieck groups of triangulated categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Peter Webb","submitted_at":"2017-09-11T01:03:06Z","abstract_excerpt":"We extend the theory of bilinear forms on the Green ring of a finite group developed by Benson and Parker to the context of the Grothendieck group of a triangulated category with Auslander-Reiten triangles, taking only relations given by direct sum decompositions. We examine the non-degeneracy of the bilinear form given by dimensions of homomorphisms, and show that the form may be modified to give a Hermitian form for which the standard basis given by indecomposable objects has a dual basis given by Auslander-Reiten triangles. An application is given to the homotopy category of perfect complex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03889","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}