{"id":"https://openalex.org/W7223961148","doi":"https://doi.org/10.48550/arxiv.2610.34398","title":"Lifting $\u03c4$-exceptional sequences","display_name":"Lifting $\u03c4$-exceptional sequences","publication_year":2026,"publication_date":"2026-10-25","ids":{"openalex":"https://openalex.org/W7223961148","doi":"https://doi.org/10.48550/arxiv.2610.34398"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.34398","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34398","pdf_url":"https://arxiv.org/pdf/2610.34398","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.34398","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078774445","display_name":"Aslak Bakke Buan","orcid":"https://orcid.org/0000-0001-6888-3434","observed_orcids":["https://orcid.org/0000-0001-6888-3434"]},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Buan, Aslak B.","raw_affiliation_strings":["School of Mathematics , University of Leeds , Leeds LS2 9JT , U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , University of Leeds , Leeds LS2 9JT , U.K","institution_ids":["https://openalex.org/I130828816"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038510773","display_name":"Eric J. Hanson","orcid":"https://orcid.org/0000-0001-8096-590X","observed_orcids":["https://orcid.org/0000-0001-8096-590X"]},"institutions":[{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Hanson, Eric J.","raw_affiliation_strings":["Department of Mathematical Sciences , Norwegian University of Science and Technology (NTNU) , 7491 Trondheim , NORWAY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Norwegian University of Science and Technology (NTNU) , 7491 Trondheim , NORWAY","institution_ids":["https://openalex.org/I204778367"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022202150","display_name":"Bethany Marsh","orcid":"https://orcid.org/0000-0002-4268-8937","observed_orcids":["https://orcid.org/0000-0002-4268-8937"]},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marsh, Bethany R.","raw_affiliation_strings":["Department of Mathematics , North Carolina State University , Raleigh , NC 27695 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , North Carolina State University , Raleigh , NC 27695 , USA","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9990000128746033,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.00019999999494757503,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/tau-tilting-theory","display_name":"\u03c4-tilting theory","score":0.878000020980835},{"id":"https://openalex.org/keywords/factor-algebras","display_name":"factor algebras","score":0.7960000038146973},{"id":"https://openalex.org/keywords/extension-of-scalars","display_name":"extension of scalars","score":0.9430000185966492},{"id":"https://openalex.org/keywords/local-algebras","display_name":"local algebras","score":0.6850000023841858},{"id":"https://openalex.org/keywords/nakayama-algebras","display_name":"Nakayama algebras","score":0.9369999766349792},{"id":"https://openalex.org/keywords/quiver-representations","display_name":"quiver representations","score":0.8450000286102295},{"id":"https://openalex.org/keywords/simple-modules","display_name":"simple modules","score":0.4690000116825104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.845300018787384},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.7879999876022339},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.7426000237464905},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.7035999894142151},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.6074000000953674},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.4864000082015991},{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.4772000014781952},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4749999940395355},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4616999924182892},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.44749999046325684},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.43950000405311584},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4334999918937683},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4050999879837036},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.39320001006126404},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37369999289512634},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3587000072002411},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.32350000739097595},{"id":"https://openalex.org/C153778094","wikidata":"https://www.wikidata.org/wiki/Q357858","display_name":"Adjoint functors","level":3,"score":0.3212999999523163},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C99633028","wikidata":"https://www.wikidata.org/wiki/Q1442189","display_name":"Natural transformation","level":3,"score":0.30489999055862427},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C148896618","wikidata":"https://www.wikidata.org/wiki/Q1426191","display_name":"Flat module","level":4,"score":0.2971999943256378},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.2890999913215637},{"id":"https://openalex.org/C18364862","wikidata":"https://www.wikidata.org/wiki/Q579978","display_name":"Homological algebra","level":3,"score":0.28679999709129333},{"id":"https://openalex.org/C31937215","wikidata":"https://www.wikidata.org/wiki/Q956233","display_name":"Simple module","level":3,"score":0.2694000005722046},{"id":"https://openalex.org/C147073270","wikidata":"https://www.wikidata.org/wiki/Q567083","display_name":"Annihilator","level":3,"score":0.2685000002384186},{"id":"https://openalex.org/C155996607","wikidata":"https://www.wikidata.org/wiki/Q381725","display_name":"Exact functor","level":3,"score":0.2653999924659729},{"id":"https://openalex.org/C48808802","wikidata":"https://www.wikidata.org/wiki/Q2007878","display_name":"Functor category","level":3,"score":0.2646999955177307},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C99463465","wikidata":"https://www.wikidata.org/wiki/Q2716519","display_name":"Injective module","level":3,"score":0.25949999690055847},{"id":"https://openalex.org/C109593458","wikidata":"https://www.wikidata.org/wiki/Q5262626","display_name":"Derived category","level":3,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.34398","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34398","pdf_url":"https://arxiv.org/pdf/2610.34398","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.2610.34398","doi":"https://doi.org/10.48550/arxiv.2610.34398","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.34398","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:2610.34398","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34398","pdf_url":"https://arxiv.org/pdf/2610.34398","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/W7223961148.pdf","grobid_xml":"https://content.openalex.org/works/W7223961148.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W6929218783","https://openalex.org/W3166814377","https://openalex.org/W4385876504","https://openalex.org/W2786466618","https://openalex.org/W3166771095","https://openalex.org/W4387520308","https://openalex.org/W7054754435","https://openalex.org/W4391940662","https://openalex.org/W4417129339","https://openalex.org/W4415183287"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,39,48,88,123,127],"behaviour":[3],"of":[4,41,51,104,126,140],"$\u03c4$-exceptional":[5,49],"sequences":[6,50],"under":[7],"passage":[8],"from":[9,47],"a":[10,15,83,107],"finite-dimensional":[11],"algebra":[12,17],"$\u039b$":[13,21],"to":[14,38,56,102,119],"factor":[16],"$\u039b/I$.":[18],"Assuming":[19],"that":[20,26],"is":[22,62,65,99],"$\u03c4$-tilting":[23],"finite":[24],"and":[25,64,72,145],"$I\\subseteq":[27],"\\operatorname{rad}\u039b$,":[28],"we":[29,81,132],"construct,":[30],"for":[31,138,146],"every":[32],"$r$":[33,53],"less":[34],"than":[35],"or":[36],"equal":[37],"number":[40],"simple":[42],"$\u039b$-modules,":[43],"an":[44,120],"injective":[45],"map":[46],"length":[52],"over":[54,58,142],"$\u039b/I$":[55],"those":[57],"$\u039b$.":[59],"The":[60],"construction":[61],"recursive":[63],"based":[66],"on":[67],"lifting":[68],"indecomposable":[69],"$\u03c4$-rigid":[70],"modules":[71],"comparing":[73],"their":[74],"associated":[75],"$\u03c4$-perpendicular":[76,90],"categories.":[77],"At":[78],"each":[79,116],"stage,":[80],"construct":[82],"right":[84],"exact":[85],"functor":[86],"between":[87],"relevant":[89],"categories":[91],"which,":[92],"after":[93],"identifying":[94],"them":[95],"with":[96,135],"module":[97],"categories,":[98],"naturally":[100],"isomorphic":[101],"extension":[103],"scalars":[105],"along":[106],"quotient":[108],"$\u0393\\to\u0393/J$,":[109],"where":[110],"$J\\subseteq":[111],"\\operatorname{rad}\u0393$.":[112],"These":[113],"functors":[114],"send":[115],"lifted":[117],"term":[118],"object":[121],"in":[122],"additive":[124],"closure":[125],"corresponding":[128],"original":[129],"term.":[130],"Finally,":[131],"conjecture":[133],"connections":[134],"known":[136],"bijections":[137],"representations":[139],"quivers":[141],"local":[143],"algebras":[144],"Nakayama":[147],"algebras.":[148]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2026-10-28T00:00:00"}