{"id":"W2783255950","doi":"","title":"Root vectors of the composition algebra of the Kronecker algebra","year":2018,"lang":"en","type":"article","venue":"The scientific electronic library of periodicals of the National Academy of Sciences of Ukraine (National Academy of Sciences of Ukraine)","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Kronecker delta; Mathematics; Cellular algebra; Algebra over a field; Realization (probability); Pure mathematics; Isomorphism (crystallography); Filtered algebra; Root of unity; Universal enveloping algebra; Symmetric algebra; Algebra representation; Combinatorics; Quantum; Physics; Crystallography; Quantum mechanics","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":["sts","open_science"],"consensus_categories":[],"category_scores_codex":[0.009221607,0.0003959671,0.0009485557,0.000663788,0.000972905,0.00004093949,0.00821525,0.0003100461,0.0003269077],"category_scores_gemma":[0.003045354,0.0002164197,0.0007321893,0.00502087,0.04145971,0.001411384,0.001450091,0.0007699682,0.000001678952],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009418128,"about_ca_system_score_gemma":0.001509198,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001755924,"about_ca_topic_score_gemma":0.000002181574,"domain_scores_codex":[0.9879007,0.0005596397,0.002671055,0.0007696277,0.007431581,0.000667392],"domain_scores_gemma":[0.9908785,0.00268958,0.005172488,0.0002875191,0.0008742754,0.00009763039],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.00006614781,0.0003753673,0.000754851,0.0002412134,0.0001113616,1.047863e-8,0.001155621,0.0009313421,0.2469796,0.7479944,0.001155221,0.0002348084],"study_design_scores_gemma":[0.0004062998,0.0002158667,0.01401668,0.0004284668,0.00005919715,0.000008773118,0.0001425871,0.001490318,0.5047854,0.4778466,0.0004415418,0.0001582559],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9738957,0.001035768,0.0000467916,0.02085621,0.0001981399,0.0008928888,0.0003683498,0.00001595257,0.00269021],"genre_scores_gemma":[0.9943919,0.0000642964,0.004674553,0.0002786588,0.0001536925,0.00001226033,0.000003000819,0.00002026967,0.0004013435],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2701478,"threshold_uncertainty_score":0.9971508,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04975219708542299,"score_gpt":0.3356265005307253,"score_spread":0.2858743034453023,"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."}}