{"paper":{"title":"On Lie algebras associated with representation directed algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Justyna Kosakowska, Stanis{\\l}aw Kasjan","submitted_at":"2009-02-19T11:31:42Z","abstract_excerpt":"Let $B$ be a representation-finite $\\mathbb{C}$-algebra.\n  The $\\mathbb{Z}$-Lie algebra $L(B)$ associated with $B$ has been defined by Ch. Riedtmann.\n  If $B$ is representation-directed there is another $\\mathbb{Z}$-Lie algebra associated with $B$ defined by C. M. Ringel and denoted by $\\CK(B)$. We prove that the Lie algebras $L(B)$ and $\\CK(B)$ are isomorphic for any representation-directed $\\mathbb{C}$-algebra $B$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.3348","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"}