{"paper":{"title":"Configurations in abelian categories. II. Ringel-Hall algebras","license":"","headline":"","cross_cats":["hep-th","math.RA","math.RT"],"primary_cat":"math.AG","authors_text":"Dominic Joyce","submitted_at":"2005-03-02T10:04:14Z","abstract_excerpt":"This is the second in a series math.AG/0312190, math.AG/0410267, math.AG/0410268 on configurations in an abelian category A. Given a finite partially ordered set (I,<), an (I,<)-configuration (\\sigma,\\iota,\\pi) is a finite collection of objects \\sigma(J) and morphisms \\iota(J,K) or \\pi(J,K) : \\sigma(J) --> \\sigma(K) in A satisfying some axioms, where J,K are subsets of I. Configurations describe how an object X in A decomposes into subobjects.\n The first paper math.AG/0312190 defined configurations and studied moduli spaces of (I,<)-configurations in A, using the theory of Artin stacks. It pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503029","kind":"arxiv","version":4},"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"}