{"paper":{"title":"Generalised friezes and a modified Caldero-Chapoton map depending on a rigid object, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Peter Jorgensen, Thorsten Holm","submitted_at":"2014-01-18T22:21:53Z","abstract_excerpt":"It is an important aspect of cluster theory that cluster categories are \"categorifications\" of cluster algebras. This is expressed formally by the (original) Caldero-Chapoton map X which sends certain objects of cluster categories to elements of cluster algebras.\n  Let \\tau c --> b --> c be an Auslander-Reiten triangle. The map X has the salient property that X(\\tau c)X(c) - X(b) = 1. This is part of the definition of a so-called frieze.\n  The construction of X depends on a cluster tilting object. In a previous paper, we introduced a modified Caldero-Chapoton map \\rho depending on a rigid obje"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4616","kind":"arxiv","version":2},"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"}