{"id":"https://openalex.org/W7220713690","doi":"https://doi.org/10.48550/arxiv.2610.05847","title":"Classification of reductive monoids","display_name":"Classification of reductive monoids","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220713690","doi":"https://doi.org/10.48550/arxiv.2610.05847"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05847","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05847","pdf_url":"https://arxiv.org/pdf/2610.05847","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/2610.05847","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038935217","display_name":"Jingren Chi","orcid":"https://orcid.org/0000-0003-3710-0665","observed_orcids":["https://orcid.org/0000-0003-3710-0665"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chi, Jingren","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5038935217"],"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9779999852180481,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9779999852180481,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.019200000911951065,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.0006000000284984708,"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/reductive-group-schemes","display_name":"reductive group schemes","score":0.8659999966621399},{"id":"https://openalex.org/keywords/weyl-group","display_name":"Weyl group","score":0.9490000009536743},{"id":"https://openalex.org/keywords/weyl-cones","display_name":"Weyl cones","score":0.9779999852180481},{"id":"https://openalex.org/keywords/descent","display_name":"descent","score":0.3779999911785126},{"id":"https://openalex.org/keywords/extension-theorems","display_name":"extension theorems","score":0.597000002861023},{"id":"https://openalex.org/keywords/quasi-split-groups","display_name":"quasi-split groups","score":0.5920000076293945},{"id":"https://openalex.org/keywords/integral-basis","display_name":"integral bases","score":0.4050000011920929}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8256000280380249},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.7422000169754028},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.691100001335144},{"id":"https://openalex.org/C179415260","wikidata":"https://www.wikidata.org/wiki/Q1006450","display_name":"Reductive group","level":3,"score":0.6855000257492065},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.682699978351593},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5932999849319458},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5600000023841858},{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.49399998784065247},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.489300012588501},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.48669999837875366},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4453999996185303},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.40849998593330383},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.3763999938964844},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3702000081539154},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35989999771118164},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.3476000130176544},{"id":"https://openalex.org/C40233952","wikidata":"https://www.wikidata.org/wiki/Q768074","display_name":"Weyl group","level":2,"score":0.3231000006198883},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.25690001249313354}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.05847","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05847","pdf_url":"https://arxiv.org/pdf/2610.05847","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.2610.05847","doi":"https://doi.org/10.48550/arxiv.2610.05847","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05847","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.05847","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05847","pdf_url":"https://arxiv.org/pdf/2610.05847","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/W7220713690.pdf","grobid_xml":"https://content.openalex.org/works/W7220713690.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7167043616"],"related_works":["https://openalex.org/W7167043616","https://openalex.org/W7161204367","https://openalex.org/W1994295709","https://openalex.org/W1920160171","https://openalex.org/W7098660335","https://openalex.org/W2034227407","https://openalex.org/W2018919932","https://openalex.org/W138998391","https://openalex.org/W7140615469","https://openalex.org/W2316566793"],"abstract_inverted_index":{"We":[0],"classify":[1],"reductive":[2,18,54],"monoids":[3,55,70,87],"over":[4,79],"arbitrary":[5],"base":[6],"schemes":[7],"by":[8],"descent":[9],"from":[10],"the":[11,47,67,85],"split":[12],"classification":[13],"in":[14],"arXiv:2607.00322.":[15],"For":[16],"a":[17,37,64,89],"group":[19,58],"scheme":[20,38],"$G$,":[21],"we":[22,62],"construct":[23,84],"its":[24],"sheaf":[25],"of":[26,39,44,49,52,69],"based":[27],"root":[28],"data,":[29],"abstract":[30,33],"Cartan":[31],"torus,":[32],"Weyl":[34,40],"group,":[35],"and":[36,83],"cones.":[41],"The":[42],"last":[43],"these":[45],"represents":[46],"functor":[48],"isomorphism":[50],"classes":[51],"rigidified":[53],"with":[56],"unit":[57],"$G$.":[59],"As":[60],"applications,":[61],"deduce":[63],"criterion":[65],"for":[66],"existence":[68],"that":[71],"are":[72],"not":[73],"groups,":[74],"prove":[75],"an":[76],"extension":[77],"theorem":[78],"normal":[80],"integral":[81],"bases,":[82],"Vinberg":[86],"without":[88],"quasi-split":[90],"hypothesis.":[91]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}