{"id":"W1994189698","doi":"10.1090/s0002-9947-09-04828-4","title":"Multiloop realization of extended affine Lie algebras and Lie tori","year":2009,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":54,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta; University of Victoria","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Affine Lie algebra; Lie conformal algebra; Pure mathematics; Lie algebra; Realization (probability); Killing form; Adjoint representation of a Lie algebra; Affine transformation; Non-associative algebra; Isomorphism (crystallography); Algebra over a field; Generalized Kac–Moody algebra; Current algebra","routes":{"ca_aff":true,"ca_fund":true,"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":[0.00037004,0.0002161709,0.0003104776,0.0004255269,0.001096396,0.001165493,0.0004882963,0.0004199506,0.002661727],"category_scores_gemma":[0.0008132472,0.0001647186,0.0004944552,0.0002666189,0.001752267,0.002084309,0.001285351,0.0008899863,0.0002648323],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005383934,"about_ca_system_score_gemma":0.000345642,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000662832,"about_ca_topic_score_gemma":0.000494339,"domain_scores_codex":[0.999602,0.00007381265,0.00002308157,0.00007801808,0.0001254734,0.00009762291],"domain_scores_gemma":[0.9996725,0.00004010997,0.00006678352,0.00007989367,0.00006128242,0.00007951164],"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":[0.00002861336,0.00001593503,0.0002663684,0.00001658926,0.00000539997,0.000253965,0.0002735363,0.001498734,0.002734522,0.9921714,0.0001915727,0.002543367],"study_design_scores_gemma":[0.00001896477,0.00006004518,0.0006553967,0.00001197929,0.00000958606,0.0003411835,0.0004869287,0.01264244,0.002775307,0.9787597,0.004215482,0.00002297542],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8758565,0.0003402198,0.0787583,0.0003097245,0.00007185796,0.00004098942,0.0001019078,0.0001549799,0.04436544],"genre_scores_gemma":[0.9903114,0.00008053062,0.006849337,0.00002685492,0.00002760126,0.00002436755,0.00007579197,0.00001356788,0.002590491],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002661727,"threshold_uncertainty_score":0.008904397,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01817150115201149,"score_gpt":0.2883774258070563,"score_spread":0.2702059246550448,"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."}}