{"id":"https://openalex.org/W7214737379","doi":"https://doi.org/10.48550/arxiv.2609.32294","title":"Global and local triviality for extensions of ample groupoids: an algebraic approach","display_name":"Global and local triviality for extensions of ample groupoids: an algebraic approach","publication_year":2026,"publication_date":"2026-09-26","ids":{"openalex":"https://openalex.org/W7214737379","doi":"https://doi.org/10.48550/arxiv.2609.32294"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.32294","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32294","pdf_url":"https://arxiv.org/pdf/2609.32294","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/2609.32294","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037086637","display_name":"Nathan Brownlowe","orcid":"https://orcid.org/0000-0001-7521-3770","observed_orcids":["https://orcid.org/0000-0001-7521-3770"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brownlowe, Nathan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017707311","display_name":"Lisa Orloff Clark","orcid":"https://orcid.org/0000-0002-0288-5178","observed_orcids":["https://orcid.org/0000-0002-0288-5178"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Clark, Lisa Orloff","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082849061","display_name":"Enrique Pardo","orcid":"https://orcid.org/0000-0002-6375-4227","observed_orcids":["https://orcid.org/0000-0002-6375-4227","https://orcid.org/0000-0002-1909-2895"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pardo, Enrique","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091380066","display_name":"Aidan Sims","orcid":"https://orcid.org/0000-0002-1965-6451","observed_orcids":["https://orcid.org/0000-0002-1965-6451"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sims, Aidan","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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9761000275611877,"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":0.9761000275611877,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.002099999925121665,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.0017000000225380063,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ample-groupoids","display_name":"ample groupoids","score":0.9409999847412109},{"id":"https://openalex.org/keywords/inverse-semigroups","display_name":"inverse semigroups","score":0.9340000152587891},{"id":"https://openalex.org/keywords/twisted-crossed-products","display_name":"twisted crossed products","score":0.8709999918937683},{"id":"https://openalex.org/keywords/local-triviality","display_name":"local triviality","score":0.9990000128746033},{"id":"https://openalex.org/keywords/c-algebras","display_name":"C*-algebras","score":0.8650000095367432}],"concepts":[{"id":"https://openalex.org/C2778795013","wikidata":"https://www.wikidata.org/wiki/Q945127","display_name":"Triviality","level":2,"score":0.9368000030517578},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6639999747276306},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.635200023651123},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6079000234603882},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5376999974250793},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5149999856948853},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.49900001287460327},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4880000054836273},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.384799987077713},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.32600000500679016},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3147999942302704},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.27649998664855957}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.32294","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32294","pdf_url":"https://arxiv.org/pdf/2609.32294","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":"pmh:oai:rodin.uca.es:10498/40292","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10498/40292","pdf_url":"https://rodin.uca.es/bitstream/10498/40292/1/2609.32294v1.pdf","source":{"id":"https://openalex.org/S4306400506","display_name":"RODIN (Universidad de C\u00e1diz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I39147953","host_organization_name":"Universidad de C\u00e1diz","host_organization_lineage":["https://openalex.org/I39147953"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Repositorio arXiv","raw_type":"journal article"},{"id":"doi:10.48550/arxiv.2609.32294","doi":"https://doi.org/10.48550/arxiv.2609.32294","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.32294","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:2609.32294","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32294","pdf_url":"https://arxiv.org/pdf/2609.32294","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/G3746902536","display_name":null,"funder_award_id":"PID2023-147110NB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4573985243","display_name":null,"funder_award_id":"21-VUW-156","funder_id":"https://openalex.org/F4320320802","funder_display_name":"Victoria University of Wellington"},{"id":"https://openalex.org/G4632184318","display_name":null,"funder_award_id":"21-VUW-156","funder_id":"https://openalex.org/F4320335369","funder_display_name":"Marsden Fund"},{"id":"https://openalex.org/G4920894121","display_name":null,"funder_award_id":"21-VUW-156","funder_id":"https://openalex.org/F4320320969","funder_display_name":"University of Wollongong"},{"id":"https://openalex.org/G763978806","display_name":null,"funder_award_id":"FQM- 298","funder_id":"https://openalex.org/F4320326754","funder_display_name":"Junta de Andaluc\u00eda"},{"id":"https://openalex.org/G8597629518","display_name":null,"funder_award_id":"ProyExcel 00780","funder_id":"https://openalex.org/F4320326754","funder_display_name":"Junta de Andaluc\u00eda"}],"funders":[{"id":"https://openalex.org/F4320309530","display_name":"Stanley Medical Research Institute","ror":"https://ror.org/01pj5nn22"},{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320320774","display_name":"Royal Society Te Ap\u0101rangi","ror":"https://ror.org/04tajb587"},{"id":"https://openalex.org/F4320320802","display_name":"Victoria University of Wellington","ror":"https://ror.org/0040r6f76"},{"id":"https://openalex.org/F4320320969","display_name":"University of Wollongong","ror":"https://ror.org/00jtmb277"},{"id":"https://openalex.org/F4320326754","display_name":"Junta de Andaluc\u00eda","ror":"https://ror.org/01jem9c82"},{"id":"https://openalex.org/F4320335369","display_name":"Marsden Fund","ror":null},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":"https://ror.org/003x0zc53"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214737379.pdf","grobid_xml":"https://content.openalex.org/works/W7214737379.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W3180054954"],"related_works":["https://openalex.org/W2952359548","https://openalex.org/W2993845873","https://openalex.org/W2045103261","https://openalex.org/W1965636134","https://openalex.org/W3122058724","https://openalex.org/W6941502243","https://openalex.org/W3047686671","https://openalex.org/W2079636963","https://openalex.org/W3113268421","https://openalex.org/W1984648834"],"abstract_inverted_index":{"Using":[0],"the":[1,4,14,20,24],"duality":[2],"between":[3],"categories":[5],"of":[6,19,23,28],"inverse":[7],"semigroups":[8],"and":[9,17],"ample":[10],"groupoids,":[11],"we":[12],"prove":[13],"triviality":[15],"(global":[16],"local)":[18],"central":[21],"term":[22],"extension":[25],"in":[26],"terms":[27],"twisted":[29],"crossed":[30],"products.":[31]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}