{"paper":{"title":"Bicharacters, braids and Jacobi identity","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"q-alg","authors_text":"Jerzy Rozanski (University of Warsaw)","submitted_at":"1996-11-22T13:33:55Z","abstract_excerpt":"For an abelian group G we consider braiding in a category of G-graded modules $M^{kG}$ given by a bicharacter \\chi on G. For $(G,\\chi)$-bialgebra A in $M^{kG}$ an analog of Lie bracket is defined. This bracket is determined by a linear map $E\\in\\End(A)$ and n-ary operations $\\Omega^{n}_{E}$ on A. Our result states that if $E(1)=0,E^{2}=0$ and $\\Omega^{3}_{E}=0$ then a braided Jacobi identity holds and the linear map E is a braided derivation of a braided Lie algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9611029","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/q-alg/9611029/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}