{"id":"W1993607200","doi":"10.1016/s0021-8693(03)00399-5","title":"Locally trivial principal homogeneous spaces and conjugacy theorems for Lie algebras","year":2003,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Conjugacy class; Homogeneous; Pure mathematics; Diagonalizable matrix; Principal (computer security); Abelian group; Combinatorics; Eigenvalues and eigenvectors; Symmetric matrix","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":[0.002125332,0.001136893,0.001349117,0.003146829,0.004347704,0.004864476,0.00119609,0.001729371,0.006299861],"category_scores_gemma":[0.003975811,0.0008234485,0.001438728,0.001924891,0.006851234,0.01067529,0.005557377,0.005257085,0.0009278101],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001760075,"about_ca_system_score_gemma":0.0008420873,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009602316,"about_ca_topic_score_gemma":0.0008571396,"domain_scores_codex":[0.9990712,0.0002561867,0.00006140886,0.0001958886,0.0002281226,0.0001871039],"domain_scores_gemma":[0.9975261,0.001086053,0.0003316558,0.0003147609,0.0002450846,0.0004963861],"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":[0.00002579367,0.0000282376,0.000205849,0.00001220224,0.000008432889,0.00007323355,0.0003962402,0.0001622888,0.000391495,0.996981,0.0002913273,0.001423867],"study_design_scores_gemma":[0.00001497052,0.00001295258,0.0001440911,0.000002511628,0.000006294458,0.00005124462,0.0001020561,0.0006242134,0.0002129177,0.998234,0.0005896,0.000005075211],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7382687,0.001345999,0.1393379,0.003357593,0.0004217383,0.0001438872,0.0002630948,0.0003173827,0.1165437],"genre_scores_gemma":[0.9676327,0.0006695263,0.009438612,0.0003772491,0.0006057051,0.00009195638,0.0002787894,0.00008509832,0.02082041],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006299861,"threshold_uncertainty_score":0.02107513,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02585205338052905,"score_gpt":0.3008343909146526,"score_spread":0.2749823375341236,"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."}}