{"id":"https://openalex.org/W7204861450","doi":"https://doi.org/10.48550/arxiv.2608.30380","title":"Morita Induction and Preservation of Geometric and Dynamical Ideals","display_name":"Morita Induction and Preservation of Geometric and Dynamical Ideals","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204861450","doi":"https://doi.org/10.48550/arxiv.2608.30380"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30380","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30380","pdf_url":"https://arxiv.org/pdf/2608.30380","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/2608.30380","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032082603","display_name":"Yeong Chyuan Chung","orcid":"https://orcid.org/0000-0001-5750-3424","observed_orcids":["https://orcid.org/0000-0001-5750-3424"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chung, Yeong Chyuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138475773","display_name":"Xinhui Du","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Du, Xinhui","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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9990000128746033,"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":0.9990000128746033,"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":0.0003000000142492354,"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":0.0,"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/morita-equivalence","display_name":"Morita equivalence","score":0.9869999885559082},{"id":"https://openalex.org/keywords/banach-algebras","display_name":"Banach algebras","score":0.8600000143051147},{"id":"https://openalex.org/keywords/closed-two-sided-ideals","display_name":"closed two-sided ideals","score":0.8209999799728394},{"id":"https://openalex.org/keywords/quotients","display_name":"quotients","score":0.6460000276565552},{"id":"https://openalex.org/keywords/etale-groupoids","display_name":"\u00e9tale groupoids","score":0.9200000166893005},{"id":"https://openalex.org/keywords/uniform-roe-algebras","display_name":"uniform Roe algebras","score":0.8360000252723694},{"id":"https://openalex.org/keywords/uniform-algebras","display_name":"uniform algebras","score":0.8240000009536743}],"concepts":[{"id":"https://openalex.org/C134941585","wikidata":"https://www.wikidata.org/wiki/Q6912366","display_name":"Morita equivalence","level":2,"score":0.8458999991416931},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8080999851226807},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7549999952316284},{"id":"https://openalex.org/C85769624","wikidata":"https://www.wikidata.org/wiki/Q2981893","display_name":"Morita therapy","level":2,"score":0.7160999774932861},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6061999797821045},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.46639999747276306},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4214000105857849},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.3995000123977661},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.37940001487731934},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37770000100135803},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.3456999957561493},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3167000114917755},{"id":"https://openalex.org/C2781106287","wikidata":"https://www.wikidata.org/wiki/Q806066","display_name":"Banach algebra","level":3,"score":0.310699999332428},{"id":"https://openalex.org/C118211362","wikidata":"https://www.wikidata.org/wiki/Q1203540","display_name":"Maximal ideal","level":3,"score":0.3059999942779541},{"id":"https://openalex.org/C9395851","wikidata":"https://www.wikidata.org/wiki/Q177929","display_name":"Stack (abstract data type)","level":2,"score":0.3021000027656555},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.29249998927116394},{"id":"https://openalex.org/C2989065042","wikidata":"https://www.wikidata.org/wiki/Q7378971","display_name":"Algebraic properties","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C129301229","wikidata":"https://www.wikidata.org/wiki/Q741865","display_name":"Uniform continuity","level":3,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30380","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30380","pdf_url":"https://arxiv.org/pdf/2608.30380","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.2608.30380","doi":"https://doi.org/10.48550/arxiv.2608.30380","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30380","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:2608.30380","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30380","pdf_url":"https://arxiv.org/pdf/2608.30380","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204861450.pdf","grobid_xml":"https://content.openalex.org/works/W7204861450.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7164339510"],"related_works":["https://openalex.org/W4396926122","https://openalex.org/W7215125838","https://openalex.org/W4414580974","https://openalex.org/W7164339510","https://openalex.org/W2057566682","https://openalex.org/W594518144","https://openalex.org/W571305812","https://openalex.org/W7099744366","https://openalex.org/W7095080702","https://openalex.org/W1598952509"],"abstract_inverted_index":{"Given":[0],"Banach":[1],"algebras":[2],"with":[3,68,123],"bounded":[4,102],"approximate":[5,103],"identities":[6],"that":[7,45,97],"are":[8,37,48],"Morita":[9,31,38,50,72,82],"equivalent":[10,39,65],"in":[11],"the":[12,21,81,85,91,98,119,140],"sense":[13],"of":[14,24,55,105,118,139],"Paravicini,":[15],"we":[16,95],"give":[17],"explicit":[18],"formulas":[19],"for":[20,131,136],"induced":[22],"correspondence":[23],"closed":[25],"ideals,":[26],"characterize":[27],"it":[28],"via":[29,40],"localized":[30],"submodules,":[32],"determine":[33],"when":[34],"corresponding":[35,46,114],"ideals":[36,76,110],"restricted":[41],"bimodules,":[42],"and":[43,77,90,112],"show":[44],"quotients":[47],"always":[49],"equivalent.":[51],"We":[52],"prove":[53,96],"preservation":[54],"geometric":[56,109],"cores":[57],"associated":[58],"to":[59],"compatible":[60],"dense":[61],"algebraic":[62],"cores.":[63],"For":[64,80],"\u00e9tale":[66],"groupoids":[67],"paracompact":[69],"unit":[70],"spaces,":[71],"induction":[73],"preserves":[74],"dynamical":[75],"inner":[78],"supports.":[79],"equivalence":[83],"between":[84],"$\\ell^p$":[86,92],"uniform":[87,93],"Roe":[88],"algebra":[89],"algebra,":[94],"latter":[99],"has":[100],"a":[101],"identity":[104],"projections,":[106],"identify":[107,113],"its":[108],"explicitly,":[111],"complete-lattice":[115],"block":[116,142],"decompositions":[117],"full":[120],"ideal":[121],"lattices":[122],"matching":[124],"extremal":[125],"ideals.":[126],"Under":[127],"property":[128,144],"A,":[129],"or":[130],"$p=1$,":[132],"these":[133],"blocks":[134],"collapse;":[135],"$p=2$,":[137],"collapse":[138],"minimal":[141],"characterizes":[143],"A.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}