{"id":"W2737744943","doi":"10.1016/j.jalgebra.2017.08.009","title":"Graded semisimple algebras are symmetric","year":2017,"lang":"en","type":"preprint","venue":"Journal of Algebra","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Institute of Infection and Immunity; Instituto de Salud Carlos III; Consiliul National al Cercetarii Stiintifice; Ontario Ministry of Research, Innovation and Science","keywords":"Mathematics; Triple system; Center (category theory); Pure mathematics; Graded ring; Symmetric algebra; Complete homogeneous symmetric polynomial; Ring of symmetric functions; Symmetric group; Division algebra; Differential graded algebra; Algebra over a field; Cellular algebra; Algebra representation","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":["metaepi_narrow","research_integrity"],"consensus_categories":[],"category_scores_codex":[0.001447545,0.0007216223,0.001883729,0.00091175,0.0002929858,0.0003596006,0.002724016,0.0008263437,0.0003016461],"category_scores_gemma":[0.007501636,0.0006371057,0.001034542,0.0002466647,0.0001984692,0.0003896924,0.001466186,0.003433261,0.00004772987],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004328993,"about_ca_system_score_gemma":0.0005081482,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007195456,"about_ca_topic_score_gemma":0.000009526073,"domain_scores_codex":[0.9952648,0.0002006198,0.001930962,0.0005456696,0.001414652,0.0006433557],"domain_scores_gemma":[0.9876095,0.001065099,0.007823769,0.002134514,0.0009582232,0.0004088897],"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":[0.0002438948,0.001327569,0.004856693,0.003546529,0.003260177,0.003031835,0.001528877,0.00008650238,0.0004078928,0.8310652,0.1325603,0.01808452],"study_design_scores_gemma":[0.0009156771,0.000115144,0.001577636,0.001178158,0.0004130792,0.0004620994,0.0001194914,0.00002100528,0.00228599,0.9863788,0.005921742,0.0006111542],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.960773,0.006291837,0.01200885,0.003020366,0.008831291,0.0009094893,0.00008466401,0.000208674,0.007871843],"genre_scores_gemma":[0.9080395,0.001219152,0.08292077,0.0003225167,0.004683543,0.00002018864,0.00001212671,0.0002932434,0.002489017],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1553136,"threshold_uncertainty_score":0.999608,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08634454699549485,"score_gpt":0.3652795048623173,"score_spread":0.2789349578668224,"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."}}