{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/124369"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/124369","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Abelianization of groupoids and Lie algebroids","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms","abstract_has_math":false,"creators":["Xiao, Shuyu"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Loja Fernandes, Rui A","Kerman, Ely","Pascaleff, James","Berwick Evans, Daniel"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-05","date_published":"2024-05","updated_at":"2026-07-22T22:25:00Z","subjects":["Abelianization","Lie Algebroid","Groupoid","Diffeology","Genus-integration"],"languages":["en","eng"],"rights":["Copyright 2024 Shuyu Xiao"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/124369","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Loja Fernandes, Rui A","Kerman, Ely","Pascaleff, James","Berwick Evans, Daniel"]},{"key":"dc:creator","label":"Author","values":["Xiao, Shuyu"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-05","2024-04-24"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Abelianization","Lie Algebroid","Groupoid","Diffeology","Genus-integration"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2024 Shuyu Xiao"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/124369"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms","The student, Shuyu Xiao, accepted the attached license on 2024-04-22 at 15:20.","The student, Shuyu Xiao, submitted this Dissertation for approval on 2024-04-22 at 15:30.","This Dissertation was approved for publication on 2024-04-24 at 15:20.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20550 on 2024-09-16 at 00:35:49","This thesis discusses abelianization of Lie algebroids and groupoids in different categories. In Chapter 2 we find a sufficient and necessary condition for a Lie algebroid to admit an abelianization and give several examps and applications. In Chapter 3 we prove that every (locally subductive) diffeological groupoid has a (locally subductive) abelianization. We also find a sufficient condition for a Lie groupoid to admit a smooth abelianization and study the smoothness of the genus-integration, the set-theoretical abelianization of the Weinstein groupoid."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Abelianization of groupoids and Lie algebroids"]}]}],"canonical_facts":{"dc:contributor":["Loja Fernandes, Rui A","Kerman, Ely","Pascaleff, James","Berwick Evans, Daniel"],"dc:creator":["Xiao, Shuyu"],"dc:date":["2024-05","2024-04-24"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms","The student, Shuyu Xiao, accepted the attached license on 2024-04-22 at 15:20.","The student, Shuyu Xiao, submitted this Dissertation for approval on 2024-04-22 at 15:30.","This Dissertation was approved for publication on 2024-04-24 at 15:20.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20550 on 2024-09-16 at 00:35:49","This thesis discusses abelianization of Lie algebroids and groupoids in different categories. In Chapter 2 we find a sufficient and necessary condition for a Lie algebroid to admit an abelianization and give several examps and applications. In Chapter 3 we prove that every (locally subductive) diffeological groupoid has a (locally subductive) abelianization. We also find a sufficient condition for a Lie groupoid to admit a smooth abelianization and study the smoothness of the genus-integration, the set-theoretical abelianization of the Weinstein groupoid."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/124369"],"dc:language":["en","eng"],"dc:rights":["Copyright 2024 Shuyu Xiao"],"dc:subject":["Abelianization","Lie Algebroid","Groupoid","Diffeology","Genus-integration"],"dc:title":["Abelianization of groupoids and Lie algebroids"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:00Z"}