{"id":"https://openalex.org/W7223223545","doi":"https://doi.org/10.48550/arxiv.2610.29539","title":"Cartan Subalgebras of Dimension Drop Interval Algebras and Their Inductive Limits","display_name":"Cartan Subalgebras of Dimension Drop Interval Algebras and Their Inductive Limits","publication_year":2026,"publication_date":"2026-10-21","ids":{"openalex":"https://openalex.org/W7223223545","doi":"https://doi.org/10.48550/arxiv.2610.29539"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.29539","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.29539","pdf_url":"https://arxiv.org/pdf/2610.29539","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/2610.29539","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159259639","display_name":"Xinlong Cui","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Cui, Xinlong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159259639"],"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.0003000000142492354,"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"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cartan-subalgebra","display_name":"Cartan subalgebra","score":0.9639999866485596},{"id":"https://openalex.org/keywords/inductive-limits","display_name":"inductive limits","score":0.703000009059906},{"id":"https://openalex.org/keywords/permutation-groups","display_name":"permutation groups","score":0.46399998664855957},{"id":"https://openalex.org/keywords/double-cosets","display_name":"double cosets","score":0.8339999914169312},{"id":"https://openalex.org/keywords/real-rank-zero","display_name":"real rank zero","score":0.6510000228881836},{"id":"https://openalex.org/keywords/stable-rank-one","display_name":"stable rank one","score":0.9580000042915344},{"id":"https://openalex.org/keywords/weyl-groupoids","display_name":"Weyl groupoids","score":0.8169999718666077},{"id":"https://openalex.org/keywords/simple-c-algebras","display_name":"simple C*-algebras","score":0.7250000238418579},{"id":"https://openalex.org/keywords/k-theory","display_name":"K-theory","score":0.7369999885559082}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8726000189781189},{"id":"https://openalex.org/C145807718","wikidata":"https://www.wikidata.org/wiki/Q2004951","display_name":"Cartan matrix","level":5,"score":0.6805999875068665},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.6628999710083008},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5745000243186951},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5077000260353088},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5076000094413757},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.40450000762939453},{"id":"https://openalex.org/C65096084","wikidata":"https://www.wikidata.org/wiki/Q2912114","display_name":"Cartan subalgebra","level":5,"score":0.3944999873638153},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.3808000087738037},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.3763999938964844},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.36809998750686646},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3377000093460083},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.32710000872612},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3237000107765198},{"id":"https://openalex.org/C87598191","wikidata":"https://www.wikidata.org/wiki/Q1571831","display_name":"Ultrafilter","level":2,"score":0.3231000006198883},{"id":"https://openalex.org/C6628132","wikidata":"https://www.wikidata.org/wiki/Q3042798","display_name":"Cartan decomposition","level":5,"score":0.2985000014305115},{"id":"https://openalex.org/C134565946","wikidata":"https://www.wikidata.org/wiki/Q906015","display_name":"Direct limit","level":2,"score":0.29179999232292175},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C4839761","wikidata":"https://www.wikidata.org/wiki/Q212111","display_name":"Spectral line","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.29539","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.29539","pdf_url":"https://arxiv.org/pdf/2610.29539","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.2610.29539","doi":"https://doi.org/10.48550/arxiv.2610.29539","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.29539","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.29539","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.29539","pdf_url":"https://arxiv.org/pdf/2610.29539","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/W7223223545.pdf","grobid_xml":"https://content.openalex.org/works/W7223223545.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2774558971","https://openalex.org/W4414289316","https://openalex.org/W2316657561","https://openalex.org/W2967558018","https://openalex.org/W1984867028","https://openalex.org/W2325215561","https://openalex.org/W2375929070","https://openalex.org/W1974694171","https://openalex.org/W2785927420","https://openalex.org/W7095886408"],"abstract_inverted_index":{"We":[0,44],"describe":[1,25],"the":[2,9,39,101,110],"conjugacy":[3,56],"of":[4,8,18,21,54,70,104],"non-degenerate":[5,36],"Cartan":[6,33,55,126],"subalgebras":[7,34],"dimension":[10],"drop":[11],"interval":[12,48],"algebras":[13],"$M_m(\\widetilde{\\mathbb":[14],"I}_p)$":[15],"in":[16,109],"terms":[17],"double":[19],"cosets":[20],"permutation":[22],"groups,":[23],"and":[24,74,81],"their":[26,114],"spectra":[27,96],"by":[28],"finite":[29,52],"bi-partite":[30],"multigraphs.":[31],"All":[32],"are":[35,42,97],"precisely":[37],"when":[38],"two":[40],"parameters":[41],"coprime.":[43],"also":[45,120],"give":[46],"splitting":[47],"examples":[49],"with":[50,78],"prescribed":[51],"numbers":[53],"classes.":[57],"Passing":[58],"to":[59,100],"inductive":[60],"limits,":[61],"we":[62],"construct":[63],"a":[64],"unital":[65],"simple":[66],"AD":[67,118],"algebra":[68,119],"$\\mathcal{A}$":[69],"real":[71],"rank":[72,76],"zero":[73],"stable":[75],"one,":[77],"$K_0(\\mathcal{A})\\cong\\mathbb":[79],"Z[1/3]$":[80],"$K_1(\\mathcal{A})\\cong\\mathbb":[82],"Z/2\\mathbb":[83],"Z$.":[84],"It":[85],"contains":[86,121],"infinitely":[87,122],"many":[88,123],"mutually":[89],"isomorphic":[90],"but":[91],"pairwise":[92,124],"nonconjugate":[93],"$\\mathrm{C}^*$-diagonals.":[94],"Their":[95],"all":[98],"homeomorphic":[99],"dense":[102],"amalgam":[103],"circles,":[105],"while":[106],"orbit":[107],"multiplicities":[108],"Weyl":[111],"groupoids":[112],"distinguish":[113],"embeddings.":[115],"The":[116],"same":[117],"nonisomorphic":[125],"subalgebras.":[127]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-23T00:00:00"}