{"id":"https://openalex.org/W7214076002","doi":"https://doi.org/10.48550/arxiv.2609.26496","title":"Coarse rigidity in von Neumann algebras via derivations","display_name":"Coarse rigidity in von Neumann algebras via derivations","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214076002","doi":"https://doi.org/10.48550/arxiv.2609.26496"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.26496","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26496","pdf_url":"https://arxiv.org/pdf/2609.26496","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/2609.26496","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152548047","display_name":"Manish Kumar","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Kumar, Manish","raw_affiliation_strings":["KU Leuven , Department of Mathematics , Celestijnenlaan 200B , 3001 Leuven , Belgium,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KU Leuven , Department of Mathematics , Celestijnenlaan 200B , 3001 Leuven , Belgium,","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074799834","display_name":"Melchior Wirth","orcid":"https://orcid.org/0000-0002-0519-4241","observed_orcids":["https://orcid.org/0000-0002-0519-4241"]},"institutions":[{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Wirth, Melchior","raw_affiliation_strings":["Mathematical Institute , Leipzig University , Augustusplatz 10 , 04109 Leipzig , Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute , Leipzig University , Augustusplatz 10 , 04109 Leipzig , Germany,","institution_ids":["https://openalex.org/I926574661"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"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":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/T11545","display_name":"Advanced Banach Space Theory","score":0.0,"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/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/von-neumann-algebras","display_name":"von Neumann algebras","score":0.9829999804496765},{"id":"https://openalex.org/keywords/quantum-markov-semigroups","display_name":"quantum Markov semigroups","score":0.8920000195503235},{"id":"https://openalex.org/keywords/ultrapowers","display_name":"ultrapowers","score":0.824999988079071},{"id":"https://openalex.org/keywords/relative-commutant","display_name":"relative commutant","score":0.8859999775886536},{"id":"https://openalex.org/keywords/indecomposability","display_name":"indecomposability","score":0.7670000195503235},{"id":"https://openalex.org/keywords/satiety","display_name":"satiety","score":0.6710000038146973},{"id":"https://openalex.org/keywords/primeness","display_name":"primeness","score":0.9829999804496765},{"id":"https://openalex.org/keywords/type-iii-von-neumann-algebras","display_name":"type III von Neumann algebras","score":0.953000009059906},{"id":"https://openalex.org/keywords/free-products-with-amalgamation","display_name":"amalgamated free products","score":0.9210000038146973},{"id":"https://openalex.org/keywords/first-cohomology-group","display_name":"first cohomology group","score":0.6489999890327454},{"id":"https://openalex.org/keywords/tempered-representations","display_name":"tempered representations","score":0.5450000166893005}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7788000106811523},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.7081999778747559},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.6872000098228455},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6448000073432922},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.6198999881744385},{"id":"https://openalex.org/C153408630","wikidata":"https://www.wikidata.org/wiki/Q1970172","display_name":"Von Neumann algebra","level":3,"score":0.4496999979019165},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.42410001158714294},{"id":"https://openalex.org/C160873635","wikidata":"https://www.wikidata.org/wiki/Q17148807","display_name":"Unital","level":3,"score":0.3774000108242035},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C100376341","wikidata":"https://www.wikidata.org/wiki/Q649977","display_name":"Jordan algebra","level":4,"score":0.3474999964237213},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.3458000123500824},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34450000524520874},{"id":"https://openalex.org/C138081561","wikidata":"https://www.wikidata.org/wiki/Q4688920","display_name":"Affiliated operator","level":5,"score":0.29739999771118164},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.27619999647140503}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.26496","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26496","pdf_url":"https://arxiv.org/pdf/2609.26496","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.2609.26496","doi":"https://doi.org/10.48550/arxiv.2609.26496","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.26496","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.26496","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26496","pdf_url":"https://arxiv.org/pdf/2609.26496","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/G3037291809","display_name":"Deformed von Neumann algebras and isomorphism problems","funder_award_id":"1221025N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214076002.pdf","grobid_xml":"https://content.openalex.org/works/W7214076002.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4286224677","https://openalex.org/W4415348190","https://openalex.org/W7077918047"],"related_works":["https://openalex.org/W3099337020","https://openalex.org/W2620491499","https://openalex.org/W7033581778","https://openalex.org/W2889206106","https://openalex.org/W7071650024","https://openalex.org/W53260465","https://openalex.org/W3111942646","https://openalex.org/W2040188953","https://openalex.org/W2971785134","https://openalex.org/W2117212310"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"the":[2,44,52,59,82],"interaction":[3],"between":[4,81],"amenability":[5],"and":[6,30,88,100,116,126,147],"first":[7],"cohomology":[8],"into":[9],"tempered":[10],"representations":[11],"of":[12,18,41,54,84,92,123],"groups,":[13],"we":[14,102],"propose":[15],"a":[16,79,104],"notion":[17],"relative":[19,65],"coarse":[20],"rigidity":[21,89],"for":[22,108],"$\u03c3$-finite":[23],"von":[24,71,132],"Neumann":[25,72,133],"algebras":[26,73,134],"through":[27],"modular":[28],"derivations":[29],"their":[31],"associated":[32,60],"GNS-symmetric":[33],"quantum":[34],"Markov":[35],"semigroups.":[36],"This":[37],"extends":[38],"Peterson's":[39],"framework":[40],"$L^2$-rigidity":[42],"to":[43,62],"nontracial":[45],"setting.":[46],"Our":[47],"main":[48],"result":[49],"shows":[50],"that":[51],"absence":[53],"relatively":[55,124,127],"amenable":[56,86],"summands":[57],"forces":[58],"deformations":[61],"converge":[63],"on":[64],"commutants":[66],"in":[67,90],"ultrapowers.":[68],"For":[69],"diffuse":[70],"with":[74,98],"separable":[75],"predual,":[76],"this":[77,96],"yields":[78],"dichotomy":[80],"presence":[83],"an":[85],"summand":[87],"terms":[91],"central":[93],"sequences.":[94],"Combining":[95],"principle":[97],"mixing":[99],"compactness,":[101],"provide":[103],"novel":[105],"unified":[106],"approach":[107],"proving":[109],"indecomposability":[110],"properties":[111],"such":[112],"as":[113],"fullness,":[114],"primeness":[115],"stable":[117],"solidity.":[118],"Applications":[119],"yield":[120],"new":[121],"examples":[122],"$\u03c9$-solid":[125],"stably":[128],"solid":[129],"type":[130],"III":[131],"arising":[135],"from":[136],"amalgamated":[137],"free":[138,141],"products,":[139,146],"operator-valued":[140],"Araki-Woods":[142],"constructions,":[143],"cocycle":[144],"crossed":[145],"twisted":[148],"nonsingular":[149],"discrete":[150],"measured":[151],"groupoids.":[152]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-24T00:00:00"}
