{"id":"W4388323198","doi":"10.1093/oso/9780199212903.003.0005","title":"Lie groups and Lie algebras","year":2009,"lang":"en","type":"book-chapter","venue":"","topic":"Molecular spectroscopy and chirality","field":"Chemistry","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Wilfrid Laurier University; University of Toronto","funders":"","keywords":"Homogeneous space; Transformation group; Pure mathematics; Simple Lie group; Lie group; Mathematics; Invariant (physics); Representation of a Lie group; Lie theory; Lie algebra; Group (periodic table); Symmetry group; Adjoint representation; Algebra over a field; Adjoint representation of a Lie algebra; Mathematical physics; Lie conformal algebra; Physics; Geometry; Quantum mechanics","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00004411141,0.0003556924,0.0003390219,0.00003023859,0.00006535974,0.00005679239,0.000176059,0.0005272459,0.01500164],"category_scores_gemma":[0.00000627614,0.0003338698,0.0001498105,0.00000706225,0.00007649483,0.0000320208,0.00008133317,0.0004764491,0.0002181503],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003991554,"about_ca_system_score_gemma":0.00003067948,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001017882,"about_ca_topic_score_gemma":0.00002076471,"domain_scores_codex":[0.9988527,0.000002787015,0.0002431479,0.0004618856,0.00021743,0.0002220446],"domain_scores_gemma":[0.999216,0.00001573865,0.000103537,0.0005078736,0.00002121502,0.0001355999],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00002310743,0.00002640996,0.00001390818,0.000151138,0.0001106178,0.0001178989,0.00002837257,3.42693e-8,0.007188024,0.9747703,0.00588722,0.01168295],"study_design_scores_gemma":[0.0003227709,0.00004853608,0.00003660632,0.0001426521,0.0001200996,0.00004434849,0.000004000893,0.000002792154,0.02749798,0.2861989,0.6849089,0.000672359],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.001425722,0.001509161,0.00005658728,0.0002042643,0.00004153734,0.00004794485,0.00001952135,0.0001409589,0.9965543],"genre_scores_gemma":[0.009062826,0.0006293408,0.0004037544,0.0008089758,0.0003706069,0.000002448475,0.00009162058,0.00005210983,0.9885783],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.6885714,"threshold_uncertainty_score":0.9999113,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009490096202915972,"score_gpt":0.2210969805965265,"score_spread":0.2116068843936106,"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."}}