{"id":"W4391112939","doi":"10.1016/j.jalgebra.2023.12.039","title":"A dichotomy between twisted tensor products of bialgebras and Frobenius algebras","year":2024,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Hausdorff Research Institute for Mathematics; Deutsche Forschungsgemeinschaft; Simons Foundation; Pacific Institute for the Mathematical Sciences; National Science Foundation","keywords":"Tensor product of algebras; Bialgebra; Mathematics; Tensor product; Frobenius algebra; Tensor product of Hilbert spaces; Pure mathematics; Tensor product of modules; Coalgebra; Tensor (intrinsic definition); Noncommutative geometry; Tensor contraction; Algebra over a field; Bimodule; Hopf 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002128423,0.0005574349,0.001183596,0.00233391,0.002878443,0.006006001,0.001444568,0.002135438,0.008798471],"category_scores_gemma":[0.004426157,0.0007711492,0.0008012524,0.002050233,0.005945399,0.01273197,0.003321473,0.003257905,0.0009719292],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001380244,"about_ca_system_score_gemma":0.0008800317,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00101947,"about_ca_topic_score_gemma":0.000775517,"domain_scores_codex":[0.9987149,0.00036697,0.00008651205,0.000202946,0.0003520747,0.0002765633],"domain_scores_gemma":[0.9973195,0.001052881,0.0003758363,0.000381119,0.0003370858,0.0005336314],"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":[0.00001684301,0.000008318922,0.00008987718,0.000007065068,0.000002193004,0.0000225364,0.0001324686,0.00006968238,0.000153615,0.9987418,0.00019345,0.0005622504],"study_design_scores_gemma":[0.000007233027,0.00000688689,0.0001082562,0.000005235903,0.000002297712,0.00005975089,0.00007006455,0.0007144036,0.00006849063,0.9985535,0.0003984764,0.000005437483],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7966291,0.002211137,0.0704788,0.006060541,0.0003860442,0.00004751063,0.0004495324,0.0002554686,0.123482],"genre_scores_gemma":[0.9841382,0.0005601332,0.00639731,0.000426441,0.0003647506,0.00004633751,0.0001811011,0.00004909868,0.007836631],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008798471,"threshold_uncertainty_score":0.02943385,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03547433262318762,"score_gpt":0.303068731557837,"score_spread":0.2675943989346494,"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."}}