{"id":"https://openalex.org/W7211908665","doi":"https://doi.org/10.48550/arxiv.2609.04275","title":"An explicit non-elementary matrix over a bivariate Laurent polynomial ring","display_name":"An explicit non-elementary matrix over a bivariate Laurent polynomial ring","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7211908665","doi":"https://doi.org/10.48550/arxiv.2609.04275"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.04275","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04275","pdf_url":"https://arxiv.org/pdf/2609.04275","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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/2609.04275","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5150623231","display_name":"Vasiliy Ionin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ionin, Vasiliy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090551196","display_name":"Artem Semidetnov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Semidetnov, Artem","raw_affiliation_strings":["Universit\u00e9 de Gen\u00e8ve , Section de Math\u00e9matiques , Route de Drize 7 , Villa Battelle , 1227 Carouge , Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Gen\u00e8ve , Section de Math\u00e9matiques , Route de Drize 7 , Villa Battelle , 1227 Carouge , Switzerland","institution_ids":["https://openalex.org/I114457229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.6621000170707703,"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":0.6621000170707703,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.2549000084400177,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.027000000700354576,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sl2","display_name":"SL2","score":0.6830000281333923},{"id":"https://openalex.org/keywords/elementary-matrices","display_name":"elementary matrices","score":0.9419999718666077},{"id":"https://openalex.org/keywords/discrete-valuation-rings","display_name":"discrete valuation rings","score":0.7059999704360962}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7462999820709229},{"id":"https://openalex.org/C106639798","wikidata":"https://www.wikidata.org/wiki/Q1701125","display_name":"Laurent polynomial","level":2,"score":0.6363000273704529},{"id":"https://openalex.org/C43169469","wikidata":"https://www.wikidata.org/wiki/Q580922","display_name":"Preprint","level":2,"score":0.6100000143051147},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.47380000352859497},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.4659000039100647},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4494999945163727},{"id":"https://openalex.org/C184311908","wikidata":"https://www.wikidata.org/wiki/Q425432","display_name":"Laurent series","level":2,"score":0.4480000138282776},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.435699999332428},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4058000147342682},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39489999413490295},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.392300009727478},{"id":"https://openalex.org/C2779873844","wikidata":"https://www.wikidata.org/wiki/Q986694","display_name":"Discrete valuation ring","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34130001068115234},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33250001072883606},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.3231000006198883},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.2985999882221222},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.2930999994277954},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.28279998898506165},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2597000002861023}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.04275","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04275","pdf_url":"https://arxiv.org/pdf/2609.04275","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.04275","doi":"https://doi.org/10.48550/arxiv.2609.04275","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.04275","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.04275","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04275","pdf_url":"https://arxiv.org/pdf/2609.04275","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7211908665.pdf","grobid_xml":"https://content.openalex.org/works/W7211908665.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1490571606","https://openalex.org/W1627662615","https://openalex.org/W1982236283","https://openalex.org/W2000170091","https://openalex.org/W2033684125","https://openalex.org/W2044818516","https://openalex.org/W2058540481","https://openalex.org/W2321006382","https://openalex.org/W4253313367"],"related_works":["https://openalex.org/W4406144068","https://openalex.org/W2145895686","https://openalex.org/W2085504080","https://openalex.org/W1993696024","https://openalex.org/W7221576935","https://openalex.org/W1986188724","https://openalex.org/W2321006382","https://openalex.org/W7165628711","https://openalex.org/W2972007679","https://openalex.org/W1984816744"],"abstract_inverted_index":{"Let":[0],"$F$":[1],"be":[2],"the":[3],"fraction":[4],"field":[5],"of":[6,21],"a":[7],"discrete":[8],"valuation":[9],"ring.":[10],"We":[11],"give":[12],"an":[13],"explicit":[14],"matrix":[15],"in":[16,31],"$\\mathrm{SL}_2(F[X^{\\pm1},Y^{\\pm1}])\\setminus":[17],"\\mathrm{E}_2(F[X^{\\pm1},Y^{\\pm1}])$.":[18],"The":[19],"proof":[20],"non-elementarity":[22],"is":[23],"based":[24],"on":[25],"techniques":[26],"developed":[27],"by":[28],"Peter":[29],"Abramenko":[30],"his":[32],"preprint":[33],"arXiv:0808.1095v1.":[34]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-08T00:00:00"}