{"id":"https://openalex.org/W7220732825","doi":"https://doi.org/10.48550/arxiv.2610.05410","title":"Embeddings of matrix algebras into the universal Roe algebra","display_name":"Embeddings of matrix algebras into the universal Roe algebra","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7220732825","doi":"https://doi.org/10.48550/arxiv.2610.05410"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05410","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05410","pdf_url":"https://arxiv.org/pdf/2610.05410","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/2610.05410","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157742200","display_name":"Hiroto Nishikawa","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nishikawa, Hiroto","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5157742200"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9984999895095825,"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":0.9984999895095825,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.000699999975040555,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.00019999999494757503,"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/uniform-roe-algebras","display_name":"uniform Roe algebras","score":0.8159999847412109},{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"matrix algebra","score":0.8659999966621399},{"id":"https://openalex.org/keywords/quasidiagonal-c-algebras","display_name":"quasidiagonal C*-algebras","score":0.8769999742507935},{"id":"https://openalex.org/keywords/permutation-operators","display_name":"permutation operators","score":0.734000027179718}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8335000276565552},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.586899995803833},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.49399998784065247},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4864000082015991},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4374000132083893},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41940000653266907},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.41499999165534973},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.375900000333786},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.34860000014305115},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.32739999890327454},{"id":"https://openalex.org/C170517529","wikidata":"https://www.wikidata.org/wiki/Q21998744","display_name":"Term algebra","level":5,"score":0.3133000135421753},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C100899422","wikidata":"https://www.wikidata.org/wiki/Q5058347","display_name":"Cellular algebra","level":4,"score":0.304500013589859},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.3043999969959259},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2973000109195709},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.29109999537467957},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C138354692","wikidata":"https://www.wikidata.org/wiki/Q1231309","display_name":"Division algebra","level":4,"score":0.2851000130176544},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.2793999910354614},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C100376341","wikidata":"https://www.wikidata.org/wiki/Q649977","display_name":"Jordan algebra","level":4,"score":0.2703000009059906},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C155058155","wikidata":"https://www.wikidata.org/wiki/Q1673406","display_name":"Universal enveloping algebra","level":3,"score":0.26429998874664307},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.2581999897956848}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.05410","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05410","pdf_url":"https://arxiv.org/pdf/2610.05410","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.2610.05410","doi":"https://doi.org/10.48550/arxiv.2610.05410","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05410","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:2610.05410","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05410","pdf_url":"https://arxiv.org/pdf/2610.05410","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":[{"id":"https://openalex.org/G8023350944","display_name":"\u7121\u9650\u30b0\u30e9\u30d5\u306e\u89e3\u6790\u7684\u6027\u8cea\u3068\u4ed8\u968f\u3059\u308b\u4f5c\u7528\u7d20\u74b0","funder_award_id":"26KJ1456","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220732825.pdf","grobid_xml":"https://content.openalex.org/works/W7220732825.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4405254461","https://openalex.org/W4405301076","https://openalex.org/W7212319228"],"related_works":["https://openalex.org/W4387252669","https://openalex.org/W4411239435","https://openalex.org/W2953394490","https://openalex.org/W2886076672","https://openalex.org/W4315926554","https://openalex.org/W4390828322","https://openalex.org/W2963284185","https://openalex.org/W4405030184","https://openalex.org/W2951193282","https://openalex.org/W1587070218"],"abstract_inverted_index":{"V.":[0],"Manuilov":[1,91],"introduced":[2,89],"the":[3,8,14,43,87,93,100,117,126,141,152,157,174],"universal":[4,44,158],"Roe":[5,10,45,65,159],"algebra,":[6,160],"namely":[7],"uniform":[9,64],"algebra":[11,46,95,102,143],"associated":[12],"with":[13,25],"largest":[15],"uniformly":[16,68,78],"locally":[17,69,79,180],"finite":[18,70,80],"coarse":[19,81],"structure":[20],"$\\mathrm{Univ}$":[21],"on":[22],"$\\mathbb{N}$,":[23],"together":[24],"several":[26],"variants.":[27],"We":[28],"study":[29],"these":[30],"algebras":[31,66],"through":[32],"embeddability":[33,84],"properties":[34,85],"of":[35,67,96,113,121,128,144,177],"$\\mathrm{C}^*$-algebras.":[36],"Among":[37],"other":[38],"results,":[39],"we":[40,107,133,147,161],"show":[41,134],"that":[42,135,163],"admits":[47],"an":[48,110],"embedding":[49],"from":[50,99],"$\\prod_n\\mathbb{M}_n$,":[51],"answering":[52],"a":[53,105],"question":[54],"by":[55,90],"Farah.":[56],"Thus,":[57],"Ozawa's":[58],"non-embeddability":[59],"theorem":[60],"for":[61,156],"$\\prod_n\\mathbb{M}_n$":[62],"in":[63],"metric":[71],"spaces":[72],"does":[73],"not":[74,149],"extend":[75],"to":[76],"arbitrary":[77],"spaces.":[82],"Nevertheless,":[83],"distinguish":[86],"variants":[88],"and":[92,171],"quasi-local":[94,142],"$\\mathrm{Univ}$,":[97],"apart":[98],"multiplier":[101],"$M(\\mathbb{I})$.":[103],"As":[104],"by-product,":[106],"also":[108],"obtain":[109],"operator-norm":[111],"analogue":[112],"Birkhoff's":[114],"Problem":[115],"111:":[116],"norm-closed":[118],"convex":[119],"hull":[120],"permutation":[122],"operators":[123],"is":[124],"exactly":[125],"set":[127],"doubly":[129],"substochastic":[130],"operators.":[131],"Moreover,":[132],"every":[136,164],"separable":[137,165],"$\\mathrm{C}^*$-algebra":[138,167,176],"embeds":[139,168],"into":[140,169,173],"$\\mathrm{Univ}$.":[145],"Although":[146],"do":[148],"know":[150],"whether":[151],"analogous":[153],"statement":[154],"holds":[155],"prove":[162],"quasidiagonal":[166],"it,":[170],"hence":[172],"reduced":[175],"some":[178],"\u00e9tale":[179],"compact":[181],"second":[182],"countable":[183],"groupoid.":[184]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}
