{"id":"https://openalex.org/W3034093496","doi":"https://doi.org/10.1142/s0218196725500195","title":"Spectrum of Rota\u2013Baxter operators","display_name":"Spectrum of Rota\u2013Baxter operators","publication_year":2025,"publication_date":"2025-05-09","ids":{"openalex":"https://openalex.org/W3034093496","doi":"https://doi.org/10.1142/s0218196725500195","mag":"3034093496"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196725500195","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196725500195","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2006.02654","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079962546","display_name":"Vsevolod Gubarev","orcid":"https://orcid.org/0000-0002-7839-5714"},"institutions":[{"id":"https://openalex.org/I188973947","display_name":"Novosibirsk State University","ror":"https://ror.org/04t2ss102","country_code":"RU","type":"education","lineage":["https://openalex.org/I188973947"]},{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Vsevolod Gubarev","raw_affiliation_strings":["Novosibirsk State University, Pirogova Str. 2, 630090, Novosibirsk, Russia","Sobolev Institute of Mathematics, Acad. Koptyug Ave. 4, 630090 Novosibirsk, Russia"],"raw_orcid":"https://orcid.org/0000-0002-7839-5714","affiliations":[{"raw_affiliation_string":"Novosibirsk State University, Pirogova Str. 2, 630090, Novosibirsk, Russia","institution_ids":["https://openalex.org/I188973947"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics, Acad. Koptyug Ave. 4, 630090 Novosibirsk, Russia","institution_ids":["https://openalex.org/I4210096862"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079962546"],"corresponding_institution_ids":["https://openalex.org/I188973947","https://openalex.org/I4210096862"],"apc_list":null,"apc_paid":null,"fwci":18.1379,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.991021,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"35","issue":"05","first_page":"687","last_page":"712"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":1.0,"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":1.0,"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":0.9954000115394592,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7443747520446777},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.6560804843902588},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.6357672214508057},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.5912987589836121},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5053094029426575},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.47576040029525757},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.44380027055740356},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3700706362724304},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3662724494934082},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3648938238620758},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13827356696128845},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07050341367721558}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7443747520446777},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.6560804843902588},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.6357672214508057},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5912987589836121},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5053094029426575},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.47576040029525757},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.44380027055740356},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3700706362724304},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3662724494934082},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3648938238620758},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13827356696128845},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07050341367721558},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218196725500195","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196725500195","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2006.02654","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.02654","pdf_url":"https://arxiv.org/pdf/2006.02654","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"mag:3034093496","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2006.02654.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2006.02654","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.02654","pdf_url":"https://arxiv.org/pdf/2006.02654","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W12818609","https://openalex.org/W584090173","https://openalex.org/W1538534850","https://openalex.org/W1598049090","https://openalex.org/W1822257168","https://openalex.org/W1829744333","https://openalex.org/W1971109247","https://openalex.org/W1982291787","https://openalex.org/W1991399360","https://openalex.org/W1996280949","https://openalex.org/W1999391790","https://openalex.org/W2007694077","https://openalex.org/W2020482247","https://openalex.org/W2041537805","https://openalex.org/W2042454346","https://openalex.org/W2068167567","https://openalex.org/W2068217923","https://openalex.org/W2072130576","https://openalex.org/W2075030330","https://openalex.org/W2094610928","https://openalex.org/W2107689143","https://openalex.org/W2110665979","https://openalex.org/W2339327824","https://openalex.org/W2554412622","https://openalex.org/W2784496575","https://openalex.org/W2917419216","https://openalex.org/W2942821138","https://openalex.org/W2963652753","https://openalex.org/W2964327692","https://openalex.org/W2992916319","https://openalex.org/W3016238707","https://openalex.org/W3102451674","https://openalex.org/W3103026326","https://openalex.org/W3105149777","https://openalex.org/W3155837056","https://openalex.org/W3158136535","https://openalex.org/W4230198387","https://openalex.org/W4234723126","https://openalex.org/W4288061039","https://openalex.org/W4312978375"],"related_works":["https://openalex.org/W2953175190","https://openalex.org/W4404619110","https://openalex.org/W2257286100","https://openalex.org/W2099602951","https://openalex.org/W4288318511","https://openalex.org/W2562705109","https://openalex.org/W2098184873","https://openalex.org/W2992850321","https://openalex.org/W2724424878","https://openalex.org/W2316101023"],"abstract_inverted_index":{"Rota\u2013Baxter":[0,35,86,108,120],"operators":[1,109],"have":[2],"been":[3],"studied":[4],"since":[5],"1960,":[6],"and":[7,19],"there":[8],"are":[9],"lots":[10],"of":[11,28,33,37,53,65,82,93,100,103,106,110],"their":[12],"applications":[13],"in":[14],"mathematical":[15],"physics,":[16],"number":[17],"theory,":[18],"noncommutative":[20],"geometry.":[21],"We":[22,57,117],"state":[23],"a":[24,43,51,79],"surprisingly":[25],"general":[26],"property":[27],"such":[29],"operators:":[30],"the":[31,63,85,98,101,119,125],"spectrum":[32],"every":[34],"operator":[36],"weight":[38,111],"[Formula:":[39,54,70,87,90,112,121,128,131,138],"see":[40,55,71,88,91,113,122,129,132,139],"text]":[41,92,114],"on":[42,74,115],"finite-dimensional":[44],"unital":[45],"(not":[46],"necessarily":[47],"associative)":[48],"algebra":[49,95,127],"is":[50,135],"subset":[52],"text].":[56,140],"even":[58],"extend":[59],"this":[60],"result":[61],"to":[62],"case":[64],"infinite-dimensional":[66],"algebraic":[67],"algebras":[68],"(when":[69],"text]).":[72],"Based":[73],"these":[75],"results,":[76],"we":[77],"define":[78],"new":[80],"invariant":[81],"an":[83,94],"algebra:":[84],"text]-index":[89,123],"A":[96],"as":[97],"infimum":[99],"degrees":[102],"minimal":[104],"polynomials":[105],"all":[107],"A.":[116],"compute":[118],"for":[124],"matrix":[126],"text],":[130],"text]:":[133],"it":[134],"shown":[136],"that":[137]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
