{"id":"W4415594031","doi":"10.1016/j.jalgebra.2025.09.044","title":"Invariant theory and coefficient algebras of Lie algebras","year":2025,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"Concordia University of Edmonton; University of Saskatchewan","funders":"National Natural Science Foundation of China; University of Saskatchewan","keywords":"Lie conformal algebra; Affine Lie algebra; Universal enveloping algebra; Subalgebra; Graded Lie algebra; Algebra representation; Representation theory; Adjoint representation of a Lie algebra; Algebra over a field; Adjoint representation","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002084782,0.0002613594,0.000734139,0.0004516044,0.00009948796,0.00004191937,0.0004943915,0.0001658212,0.0002085393],"category_scores_gemma":[0.003008362,0.0002136383,0.0002119437,0.0004428826,0.0002999196,0.0002286375,0.0002407083,0.0005122573,0.000005299799],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008841636,"about_ca_system_score_gemma":0.0002517852,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001494442,"about_ca_topic_score_gemma":0.000002943482,"domain_scores_codex":[0.9974357,0.0002704551,0.001257631,0.0002289435,0.0004965222,0.0003107632],"domain_scores_gemma":[0.995833,0.002152927,0.0009916847,0.00047002,0.0004075048,0.0001448933],"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":[0.0001796188,0.0002631991,0.0004599809,0.0002040824,0.0002697425,0.00004655293,0.0006109388,0.000007415203,0.002575733,0.9891532,0.00226693,0.003962621],"study_design_scores_gemma":[0.00114355,0.0002242622,0.00119524,0.0004249363,0.0002052732,0.000135038,0.0005412884,0.0000231929,0.02162338,0.9726836,0.001621468,0.0001787415],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8986219,0.002294393,0.09223771,0.0008938606,0.0007787467,0.0002704071,0.000007163399,0.00003465952,0.004861142],"genre_scores_gemma":[0.9622134,0.0002462071,0.03579659,0.0005010384,0.0001807445,0.000003808964,8.234115e-7,0.00004041306,0.001016973],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06359148,"threshold_uncertainty_score":0.8711916,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02052286276325875,"score_gpt":0.3113545363057261,"score_spread":0.2908316735424673,"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."}}