{"id":"https://openalex.org/W7204835464","doi":"https://doi.org/10.48550/arxiv.2608.28257","title":"On Locally Finite Derivations in Ore Extensions","display_name":"On Locally Finite Derivations in Ore Extensions","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204835464","doi":"https://doi.org/10.48550/arxiv.2608.28257"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28257","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28257","pdf_url":"https://arxiv.org/pdf/2608.28257","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.28257","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136686539","display_name":"R. Baltazar","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Baltazar, R.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148827871","display_name":"A. Bianchi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bianchi, A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148819767","display_name":"M. Veloso","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Veloso, M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138428686","display_name":"J. Schwarz","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schwarz, J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9897000193595886,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9897000193595886,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.006399999838322401,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.0010000000474974513,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/ore-extensions","display_name":"Ore extensions","score":0.9779999852180481},{"id":"https://openalex.org/keywords/quantum-plane","display_name":"quantum plane","score":0.6930000185966492},{"id":"https://openalex.org/keywords/quantum-weyl-algebra","display_name":"quantum Weyl algebra","score":0.8980000019073486},{"id":"https://openalex.org/keywords/generalized-weyl-algebras","display_name":"generalized Weyl algebras","score":0.9649999737739563},{"id":"https://openalex.org/keywords/lie-algebras-of-derivations","display_name":"Lie algebras of derivations","score":0.8209999799728394},{"id":"https://openalex.org/keywords/noncommutative-polynomial-algebras","display_name":"noncommutative polynomial algebras","score":0.8109999895095825}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7430999875068665},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.73089998960495},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.6460000276565552},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5766000151634216},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.574999988079071},{"id":"https://openalex.org/C2779152781","wikidata":"https://www.wikidata.org/wiki/Q1069378","display_name":"Weyl algebra","level":3,"score":0.557699978351593},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.5245000123977661},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.46129998564720154},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41100001335144043},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.40380001068115234},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3937999904155731},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.3555000126361847},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.3456999957561493},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.34369999170303345},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.3188999891281128},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.3167000114917755},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C56802139","wikidata":"https://www.wikidata.org/wiki/Q149999","display_name":"Differential calculus","level":2,"score":0.2992999851703644},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2791000008583069},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.2784999907016754},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25850000977516174}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28257","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28257","pdf_url":"https://arxiv.org/pdf/2608.28257","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.28257","doi":"https://doi.org/10.48550/arxiv.2608.28257","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28257","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.28257","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28257","pdf_url":"https://arxiv.org/pdf/2608.28257","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204835464.pdf","grobid_xml":"https://content.openalex.org/works/W7204835464.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7213613151","https://openalex.org/W2472660427","https://openalex.org/W4241004292","https://openalex.org/W7164233941","https://openalex.org/W2074094231","https://openalex.org/W2049158034","https://openalex.org/W7171365246","https://openalex.org/W4367298631","https://openalex.org/W2046689145","https://openalex.org/W7099022436"],"abstract_inverted_index":{"Let":[0],"$\\Bbbk$":[1],"be":[2],"an":[3],"algebraically":[4],"closed":[5],"field":[6],"of":[7,16,20,49,52,98,142,153],"characteristic":[8],"zero.":[9],"We":[10],"classify":[11],"the":[12,30,42,47,54,57,63,72,76,83,90,96,108,121],"locally":[13,84,138,148],"finite":[14,85,139,149],"derivations":[15,86],"arbitrary":[17],"Ore":[18,50,65],"extensions":[19,51,66],"$\\Bbbk[x]$,":[21],"thus":[22],"extending":[23],"van":[24],"den":[25],"Essen's":[26],"\\cite{V92}":[27],"classification":[28,48,118],"for":[29],"polynomial":[31],"algebra":[32],"$\\Bbbk[x,y]$":[33],"to":[34,95],"this":[35],"noncommutative":[36],"setting.":[37],"More":[38],"precisely,":[39],"we":[40,81,114,129],"consider":[41],"three":[43],"families":[44],"arising":[45],"in":[46,119],"$\\Bbbk[x]$:":[53],"quantum":[55,59,73,78],"plane,":[56],"first":[58,77],"Weyl":[60,79,105],"algebra,":[61,80],"and":[62,75,87,100,123,136],"differential":[64],"\\[":[67],"A_h=\\Bbbk[x][t;h(x)\\partial_x].":[68],"\\]":[69],"For":[70,107],"both":[71,120],"plane":[74],"determine":[82],"explain":[88],"how":[89],"resulting":[91],"classifications":[92],"are":[93],"related":[94],"work":[97],"Su\u00e1rez-Alvarez":[99],"Vivas":[101],"\\cite{SuarezVivas}":[102],"on":[103],"generalized":[104],"algebras.":[106],"algebras":[109],"$A_h$,":[110],"with":[111],"$h$":[112],"nonconstant,":[113],"obtain":[115],"a":[116,127,134,151],"complete":[117],"square-free":[122],"non-square-free":[124],"cases.":[125],"As":[126],"consequence,":[128],"show":[130],"that":[131],"$\\LFD(A_h)$":[132],"is":[133,146],"solvable":[135],"weakly":[137],"Lie":[140],"subalgebra":[141],"$\\Der(A_h)$,":[143],"although":[144],"it":[145],"not":[147],"as":[150],"set":[152],"derivations.":[154]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-01T00:00:00"}