{"id":"W2150987253","doi":"10.1016/j.jpaa.2005.06.007","title":"The centroid of extended affine and root graded Lie algebras","year":2005,"lang":"en","type":"article","venue":"Journal of Pure and Applied Algebra","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":68,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Ottawa","funders":"","keywords":"Mathematics; Affine transformation; Affine Lie algebra; Centroid; Adjoint representation of a Lie algebra; Pure mathematics; Lie conformal algebra; Lie algebra; Killing form; Root (linguistics); Representation of a Lie group; Graded Lie algebra; Algebra over a field; Current algebra; Linguistics; Geometry","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009174542,0.0005181457,0.001328039,0.002207399,0.002063024,0.003245129,0.001676788,0.001171596,0.007988327],"category_scores_gemma":[0.003212461,0.0003682005,0.0005447694,0.00138441,0.003301718,0.006117421,0.002380894,0.001695388,0.001120573],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001704468,"about_ca_system_score_gemma":0.001014786,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002028278,"about_ca_topic_score_gemma":0.001732155,"domain_scores_codex":[0.9994276,0.00009156387,0.00003472702,0.0001255518,0.0001820378,0.0001384805],"domain_scores_gemma":[0.9988827,0.0001879194,0.0002439274,0.00009733418,0.0002750299,0.0003130817],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002688147,0.00000752558,0.000118888,0.00001305638,0.000003995429,0.00004141213,0.0001892291,0.0003729997,0.0006725924,0.9956032,0.0003886073,0.002561645],"study_design_scores_gemma":[0.00001739119,0.00002225738,0.0004171598,0.00000690345,0.00000650479,0.0001058948,0.0001511458,0.003015165,0.0005976422,0.9922241,0.003418431,0.00001742149],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7768406,0.002495001,0.1152109,0.001788996,0.0007166974,0.00007307504,0.00041225,0.000403444,0.102059],"genre_scores_gemma":[0.9560149,0.0007102754,0.01093111,0.0002095725,0.0005257244,0.0000337449,0.0002628934,0.0001304819,0.0311814],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007988327,"threshold_uncertainty_score":0.02672362,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01732211470938698,"score_gpt":0.2754368130659955,"score_spread":0.2581146983566085,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}