{"id":"https://openalex.org/W7221834550","doi":"https://doi.org/10.48550/arxiv.2610.16300","title":"Derivation based noncommutative geometry of quiver path algebras","display_name":"Derivation based noncommutative geometry of quiver path algebras","publication_year":2026,"publication_date":"2026-10-12","ids":{"openalex":"https://openalex.org/W7221834550","doi":"https://doi.org/10.48550/arxiv.2610.16300"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.16300","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16300","pdf_url":"https://arxiv.org/pdf/2610.16300","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/2610.16300","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005188359","display_name":"Joakim Arnlind","orcid":"https://orcid.org/0000-0002-8727-2169","observed_orcids":["https://orcid.org/0000-0002-8727-2169"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arnlind, Joakim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5092829344","display_name":"Victor Hildebrandsson","orcid":"https://orcid.org/0009-0008-9016-2228","observed_orcids":["https://orcid.org/0009-0008-9016-2228"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hildebrandsson, Victor","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":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/T11673","display_name":"Advanced Topics in Algebra","score":0.4108999967575073,"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"}},"topics":[{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.4108999967575073,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.2985999882221222,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.14419999718666077,"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/noncommutative-geometry","display_name":"noncommutative geometry","score":0.9300000071525574},{"id":"https://openalex.org/keywords/derivations","display_name":"derivations","score":0.9190000295639038},{"id":"https://openalex.org/keywords/lie-algebras-of-derivations","display_name":"Lie algebras of derivations","score":0.8730000257492065},{"id":"https://openalex.org/keywords/differential-calculus","display_name":"differential calculus","score":0.9860000014305115},{"id":"https://openalex.org/keywords/levi-civita-connection","display_name":"Levi-Civita connection","score":0.9010000228881836},{"id":"https://openalex.org/keywords/torsion-free-connections","display_name":"torsion-free connections","score":0.9039999842643738}],"concepts":[{"id":"https://openalex.org/C135658033","wikidata":"https://www.wikidata.org/wiki/Q2903821","display_name":"Bimodule","level":3,"score":0.95169997215271},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.8959000110626221},{"id":"https://openalex.org/C168310172","wikidata":"https://www.wikidata.org/wiki/Q493980","display_name":"Quiver","level":2,"score":0.7919999957084656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6840000152587891},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.5845000147819519},{"id":"https://openalex.org/C193645952","wikidata":"https://www.wikidata.org/wiki/Q7049219","display_name":"Noncommutative algebraic geometry","level":4,"score":0.5601000189781189},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.541100025177002},{"id":"https://openalex.org/C56802139","wikidata":"https://www.wikidata.org/wiki/Q149999","display_name":"Differential calculus","level":2,"score":0.5393000245094299},{"id":"https://openalex.org/C139080492","wikidata":"https://www.wikidata.org/wiki/Q7756337","display_name":"Differential algebra","level":2,"score":0.49709999561309814},{"id":"https://openalex.org/C115071613","wikidata":"https://www.wikidata.org/wiki/Q1047080","display_name":"Differential form","level":2,"score":0.4936000108718872},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.47679999470710754},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4641999900341034},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.45680001378059387},{"id":"https://openalex.org/C52465356","wikidata":"https://www.wikidata.org/wiki/Q7269034","display_name":"Quantum differential calculus","level":4,"score":0.42980000376701355},{"id":"https://openalex.org/C49976459","wikidata":"https://www.wikidata.org/wiki/Q17103517","display_name":"Spectral triple","level":4,"score":0.4284000098705292},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.427700012922287},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.42480000853538513},{"id":"https://openalex.org/C60321788","wikidata":"https://www.wikidata.org/wiki/Q1197190","display_name":"Multilinear algebra","level":5,"score":0.3822000026702881},{"id":"https://openalex.org/C29384965","wikidata":"https://www.wikidata.org/wiki/Q7049223","display_name":"Noncommutative quantum field theory","level":3,"score":0.35830000042915344},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3553999960422516},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.26600000262260437}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.16300","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16300","pdf_url":"https://arxiv.org/pdf/2610.16300","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.2610.16300","doi":"https://doi.org/10.48550/arxiv.2610.16300","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.16300","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:2610.16300","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16300","pdf_url":"https://arxiv.org/pdf/2610.16300","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/W7221834550.pdf","grobid_xml":"https://content.openalex.org/works/W7221834550.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391939029","https://openalex.org/W3106281461","https://openalex.org/W2998512164","https://openalex.org/W2988366090","https://openalex.org/W7122561903","https://openalex.org/W4416528467","https://openalex.org/W1984254007","https://openalex.org/W2952633048","https://openalex.org/W7096196737","https://openalex.org/W2081856598"],"abstract_inverted_index":{"In":[0,46],"this":[1],"paper,":[2],"we":[3,56,105],"study":[4],"derivation":[5],"based":[6],"noncommutative":[7,92],"geometry":[8],"of":[9,20,33,43,52,69,94,101,109],"path":[10],"algebras":[11],"arising":[12],"from":[13,22],"quivers":[14,110],"by":[15,48],"identifying":[16],"a":[17,24,53,58,73,107,124],"Lie":[18],"algebra":[19],"derivations":[21],"which":[23,63,89,112],"differential":[25,35,70],"calculus":[26,36],"is":[27,64],"constructed.":[28],"We":[29],"show":[30],"that":[31],"properties":[32],"the":[34,41,44,50,61,67,95,102],"are":[37],"intimately":[38],"connected":[39],"with":[40,123],"structure":[42],"quiver.":[45],"particular,":[47],"introducing":[49],"notion":[51],"separating":[54],"quiver,":[55],"find":[57],"condition":[59],"on":[60],"quiver":[62],"equivalent":[65],"to":[66],"module":[68],"forms":[71,88],"being":[72],"projective":[74],"bimodule.":[75],"For":[76],"such":[77],"quivers,":[78],"one":[79,113],"can":[80,114],"construct":[81,115],"bimodule":[82,87,125],"connections,":[83,117],"as":[84,86,91],"well":[85],"serve":[90],"analogues":[93],"Riemannian":[96],"metric.":[97],"As":[98],"an":[99],"illustration":[100],"above":[103],"concepts,":[104],"present":[106],"class":[108],"for":[111],"Levi-Civita":[116],"i.e.":[118],"torsion":[119],"free":[120],"connections":[121],"compatible":[122],"form.":[126]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-15T00:00:00"}