{"id":"W2109498994","doi":"10.1142/s0219498813500692","title":"ON A FORMULA FOR THE PI-EXPONENT OF LIE ALGEBRAS","year":2013,"lang":"en","type":"preprint","venue":"Journal of Algebra and Its Applications","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Vlaamse regering; Memorial University of Newfoundland; Fonds Wetenschappelijk Onderzoek","keywords":"Mathematics; Exponent; Lie algebra; Pure mathematics; Nilpotent; Automorphism; Hopf algebra; Lie group; Simple Lie group; Nilpotent group; Algebra over a field","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004522537,0.0002654413,0.0005644161,0.0001554561,0.0001649049,0.00005308418,0.0006543223,0.0002237819,0.00005931668],"category_scores_gemma":[0.000552766,0.0001742026,0.0003117558,0.0001001951,0.00008781887,0.00009751898,0.0002700297,0.0006721116,0.000006999609],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006283735,"about_ca_system_score_gemma":0.0001310495,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001678335,"about_ca_topic_score_gemma":0.000001652732,"domain_scores_codex":[0.9981425,0.00003200599,0.001018066,0.0002317184,0.0003685737,0.0002071576],"domain_scores_gemma":[0.9944893,0.002417671,0.00171651,0.0006309932,0.0006313912,0.0001141923],"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":[0.00002870982,0.0002218374,0.00000426341,0.0003662263,0.0002401371,3.418849e-7,0.000313727,0.00003572649,0.000325949,0.9882436,0.003755926,0.006463569],"study_design_scores_gemma":[0.0004473388,0.0001691259,0.000113752,0.0002219092,0.0002747731,0.00001574686,0.0001043798,0.0002858875,0.002531933,0.9859461,0.009721818,0.000167206],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4496204,0.006293395,0.5295671,0.006965872,0.0006308982,0.005598978,0.0001723235,0.00004863657,0.001102347],"genre_scores_gemma":[0.9210792,0.002802938,0.07246225,0.0003900223,0.001092093,0.001209891,0.00001340117,0.0001117908,0.0008383871],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.4714588,"threshold_uncertainty_score":0.7103775,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0534985842795777,"score_gpt":0.3410355020291383,"score_spread":0.2875369177495606,"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."}}