{"id":"W2963523350","doi":"10.14712/1213-7243.2015.188","title":"Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions","year":2017,"lang":"en","type":"article","venue":"Commentationes Mathematicae Universitatis Carolinae","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Division of Mathematical Sciences; Natural Sciences and Engineering Research Council of Canada; Pacific Institute for the Mathematical Sciences; University of Saskatchewan","keywords":"Mathematics; Multilinear map; Isomorphism (crystallography); Group (periodic table); Combinatorics; Representation theory; Polynomial; Degree (music); Invariant theory; Symmetric group; Algebra over a field; Constructive; Discrete mathematics; Pure mathematics; Computer science","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":["sts"],"consensus_categories":[],"category_scores_codex":[0.0003498525,0.0002287832,0.0002907847,0.0001044802,0.002574835,0.0001310556,0.00168843,0.00005934239,0.0000333433],"category_scores_gemma":[0.0007002704,0.0001250854,0.0001920397,0.0002639216,0.0005084603,0.0002651792,0.0003110444,0.0001447742,0.000002248164],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001006157,"about_ca_system_score_gemma":0.00003807108,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000110633,"about_ca_topic_score_gemma":0.0002155018,"domain_scores_codex":[0.9987674,0.0000764835,0.0003418763,0.000245456,0.0003111206,0.0002576251],"domain_scores_gemma":[0.989574,0.008053772,0.0006271896,0.001432001,0.0002590113,0.00005407936],"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":[0.00007013651,0.0000638531,0.0002275923,0.0001901049,0.0002695655,1.952863e-7,0.00292587,0.00003276626,0.00006297766,0.9897498,0.004440655,0.001966432],"study_design_scores_gemma":[0.001453873,0.0001385626,0.005796867,0.00007502004,0.0009366355,0.0000102101,0.01091923,0.0003732238,0.0003952849,0.9755479,0.004115081,0.0002381169],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02252844,0.0001281706,0.9632185,0.006411516,0.0004009869,0.005961987,0.0007762138,0.00004979523,0.0005244341],"genre_scores_gemma":[0.8605052,0.00002843625,0.1361621,0.0004854913,0.0002043883,0.0009163487,0.00003883678,0.0000744725,0.00158482],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8379767,"threshold_uncertainty_score":0.9987237,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0352176826892751,"score_gpt":0.3207212047547561,"score_spread":0.285503522065481,"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."}}