{"id":"https://openalex.org/W50890759","doi":null,"title":"Schur's Lemma is False for Differential Operators","display_name":"Schur's Lemma is False for Differential Operators","publication_year":2007,"publication_date":"2007-03-01","ids":{"openalex":"https://openalex.org/W50890759","mag":"50890759"},"language":"en","primary_location":{"id":"mag:50890759","doi":null,"is_oa":false,"landing_page_url":"https://vixra.org/pdf/0703.0010v1.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2883122597","display_name":"viXra","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"viXra","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044360698","display_name":"Thomas R. Love","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Thomas R. Love","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5044360698"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.6782000064849854,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.6782000064849854,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.093299999833107,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.07970000058412552,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/schur-s-lemma","display_name":"Schur's lemma","score":0.9900000095367432},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.7319999933242798},{"id":"https://openalex.org/keywords/first-order-differential-operators","display_name":"first-order differential operators","score":0.8769999742507935},{"id":"https://openalex.org/keywords/su-2-representations","display_name":"SU(2) representations","score":0.8410000205039978},{"id":"https://openalex.org/keywords/representations-of-lie-algebras","display_name":"Lie algebra representations","score":0.5230000019073486},{"id":"https://openalex.org/keywords/differential-operators-on-manifolds","display_name":"differential operators on manifolds","score":0.49900001287460327}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7925870418548584},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5729600787162781},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5247007608413696},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3576878309249878},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3493064045906067},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.17654800415039062},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.173959881067276},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0652121901512146},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:50890759","doi":null,"is_oa":false,"landing_page_url":"https://vixra.org/pdf/0703.0010v1.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2883122597","display_name":"viXra","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"viXra","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2962922956","https://openalex.org/W2129337328","https://openalex.org/W2962821075","https://openalex.org/W7096148907","https://openalex.org/W6967120959","https://openalex.org/W2263098383","https://openalex.org/W1963818364","https://openalex.org/W2023783684","https://openalex.org/W2513577553","https://openalex.org/W1999775125"],"abstract_inverted_index":{"We":[0],"construct":[1],"two":[2],"first":[3],"order":[4],"differential":[5],"operators":[6,11],"which":[7],"commute":[8],"with":[9],"the":[10],"in":[12],"a":[13,18],"representation":[14],"of":[15],"su(2),":[16],"providing":[17],"counterexample":[19],"to":[20],"Schur\ufffds":[21],"Lemma.":[22]},"counts_by_year":[],"updated_date":"2025-10-10T17:16:08.811792","created_date":"2016-06-24T00:00:00"}
