{"id":"https://openalex.org/W2035476823","doi":"https://doi.org/10.1142/s0218196709005172","title":"UNIVERSAL ALGEBRA OF SECTORS","display_name":"UNIVERSAL ALGEBRA OF SECTORS","publication_year":2009,"publication_date":"2009-05-01","ids":{"openalex":"https://openalex.org/W2035476823","doi":"https://doi.org/10.1142/s0218196709005172","mag":"2035476823"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196709005172","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005172","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":["crossref"],"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/A5007465802","display_name":"Katsunori Kawamura","orcid":"https://orcid.org/0000-0003-1538-4273"},"institutions":[{"id":"https://openalex.org/I135768898","display_name":"Ritsumeikan University","ror":"https://ror.org/0197nmd03","country_code":"JP","type":"education","lineage":["https://openalex.org/I135768898","https://openalex.org/I4390039241"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"KATSUNORI KAWAMURA","raw_affiliation_strings":["College of Science and Engineering, Ritsumeikan University, 1-1-1 Noji Higashi, Kusatsu, Shiga 525-8577, Japan","College of Science and Engineering, Ritsumeikan University, 1-1-1, Noji-higashi, Kusatsu, Shiga 525-8577, Japan"],"affiliations":[{"raw_affiliation_string":"College of Science and Engineering, Ritsumeikan University, 1-1-1 Noji Higashi, Kusatsu, Shiga 525-8577, Japan","institution_ids":["https://openalex.org/I135768898"]},{"raw_affiliation_string":"College of Science and Engineering, Ritsumeikan University, 1-1-1, Noji-higashi, Kusatsu, Shiga 525-8577, Japan","institution_ids":["https://openalex.org/I135768898"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007465802"],"corresponding_institution_ids":["https://openalex.org/I135768898"],"apc_list":null,"apc_paid":null,"fwci":0.8172,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.67249126,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"19","issue":"03","first_page":"347","last_page":"371"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":1.0,"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":0.9991999864578247,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.8119566440582275},{"id":"https://openalex.org/keywords/unital","display_name":"Unital","score":0.6493271589279175},{"id":"https://openalex.org/keywords/subalgebra","display_name":"Subalgebra","score":0.6474001407623291},{"id":"https://openalex.org/keywords/quotient-algebra","display_name":"Quotient algebra","score":0.5834444165229797},{"id":"https://openalex.org/keywords/endomorphism","display_name":"Endomorphism","score":0.5483471155166626},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.48746395111083984},{"id":"https://openalex.org/keywords/universal-algebra","display_name":"Universal algebra","score":0.4501575529575348},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.43000149726867676},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3995002508163452},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.3335515558719635},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33052417635917664},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33007970452308655}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8119566440582275},{"id":"https://openalex.org/C160873635","wikidata":"https://www.wikidata.org/wiki/Q17148807","display_name":"Unital","level":3,"score":0.6493271589279175},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.6474001407623291},{"id":"https://openalex.org/C51287006","wikidata":"https://www.wikidata.org/wiki/Q63565120","display_name":"Quotient algebra","level":4,"score":0.5834444165229797},{"id":"https://openalex.org/C116858840","wikidata":"https://www.wikidata.org/wiki/Q1340800","display_name":"Endomorphism","level":2,"score":0.5483471155166626},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.48746395111083984},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.4501575529575348},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43000149726867676},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3995002508163452},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.3335515558719635},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33052417635917664},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33007970452308655},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196709005172","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005172","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1489334106","https://openalex.org/W1511812244","https://openalex.org/W1514324498","https://openalex.org/W1524878283","https://openalex.org/W1968436506","https://openalex.org/W1991831588","https://openalex.org/W1994416201","https://openalex.org/W1995462426","https://openalex.org/W1996167139","https://openalex.org/W2019048430","https://openalex.org/W2043485873","https://openalex.org/W2073990535","https://openalex.org/W2077811938","https://openalex.org/W2086191654","https://openalex.org/W2131336344","https://openalex.org/W2145607422","https://openalex.org/W2154239625","https://openalex.org/W2363506000","https://openalex.org/W2963463563","https://openalex.org/W3098353648","https://openalex.org/W4210846155","https://openalex.org/W4213165878","https://openalex.org/W4231199984","https://openalex.org/W4253206617","https://openalex.org/W4254718852"],"related_works":["https://openalex.org/W4327509080","https://openalex.org/W3127107065","https://openalex.org/W2742046838","https://openalex.org/W3196739338","https://openalex.org/W2987699141","https://openalex.org/W2902241454","https://openalex.org/W4289242551","https://openalex.org/W3199132729","https://openalex.org/W2314313762","https://openalex.org/W1697983944"],"abstract_inverted_index":{"We":[0,36],"show":[1,37,140],"that":[2,38,92,141],"a":[3,15,22,25,52,79,111],"nontrivial":[4],"example":[5],"of":[6,29,32,44,47,98,103,106,114,122,125,132,144,154],"universal":[7,53],"algebra":[8,54,74],"appears":[9],"in":[10],"quantum":[11],"field":[12],"theory.":[13],"For":[14],"unital":[16,30,104],"C":[17,80],"*-algebra":[18],"[Formula:":[19,33,41,48,68,75,95,107,115,133,145,149,155],"see":[20,34,42,49,69,76,96,108,116,134,146,150,156],"text],":[21],"sector":[23],"is":[24,51,60,110,127],"unitary":[26,100],"equivalence":[27,101],"class":[28],"*-endomorphisms":[31],"text].":[35,117,135,157],"the":[39,72,93,142],"set":[40,94],"text]":[43,50,70,77,97,109,147,151],"all":[45,99],"sectors":[46],"with":[55,82],"an":[56,137],"N-ary":[57],"sum":[58,66],"which":[59],"not":[61],"reduced":[62],"to":[63],"any":[64],"binary":[65],"when":[67],"includes":[71],"Cuntz":[73],"as":[78],"*-subalgebra":[81],"common":[83],"unit":[84],"for":[85],"N":[86],"\u2265":[87],"3.":[88],"Next":[89],"we":[90,139],"explain":[91],"classes":[102],"*-representations":[105],"right":[112],"module":[113],"An":[118],"essential":[119],"algebraic":[120],"formulation":[121],"branching":[123],"laws":[124],"representations":[126],"given":[128],"by":[129],"using":[130],"submodules":[131],"As":[136],"application,":[138],"action":[143],"on":[148],"distinguishes":[152],"elements":[153]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
