{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/129932"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/129932","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Analytic and holomorphic structures in Lie groupoids, algebroids, and Poisson geometry","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","abstract_has_math":false,"creators":["Jiang, Ning"],"institution":"University of Illinois Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Fernandes, Rui Loja","Albin, Pierre","Lerman, Eugene","Tolman, Susan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-07-16","date_published":"2025-07-16","updated_at":"2026-07-22T22:25:06Z","subjects":["Poisson Geometry","Complex Geometry","Lie Groupoid","Lie Algebroid"],"languages":["en","eng"],"rights":["Copyright 2025 Ning Jiang"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/129932","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Fernandes, Rui Loja","Albin, Pierre","Lerman, Eugene","Tolman, Susan"]},{"key":"dc:creator","label":"Author","values":["Jiang, Ning"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-07-16","2025-08"]},{"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 Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Poisson Geometry","Complex Geometry","Lie Groupoid","Lie Algebroid"]}]},{"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 2025 Ning Jiang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/129932"]}]},{"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 2025-10-20 without embargo terms","The student, Ning Jiang, accepted the attached license on 2025-07-14 at 13:10.","The student, Ning Jiang, submitted this Dissertation for approval on 2025-07-14 at 13:17.","This Dissertation was approved for publication on 2025-07-16 at 15:57.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22502 on 2025-10-20 at 20:15:09","This thesis explores analytic and holomorphic structures in Lie groupoids, Lie algebroids, and Poisson geometry. The first chapter provides background material on Lie groupoids, Lie algebroids, and Poisson structures. In the second chapter, we prove that any analytic s-proper Lie groupoid is analytically linearizable. Our approach relies on constructing an analytic Haar density and an analytic 2-metric on groupoids. The third chapter introduces the notion of complexification for analytic Lie algebroids. We establish that when the anchor map is injective or surjective, the integrability of the original algebroid implies the integrability of its complexification. Moreover, if the analytic algebroid is of s-proper type, its complexification is locally integrable. In the fourth chapter, we develop a computer program for computing the holomorphic Poisson cohomology of projective spaces."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Analytic and holomorphic structures in Lie groupoids, algebroids, and Poisson geometry"]}]}],"canonical_facts":{"dc:contributor":["Fernandes, Rui Loja","Albin, Pierre","Lerman, Eugene","Tolman, Susan"],"dc:creator":["Jiang, Ning"],"dc:date":["2025-07-16","2025-08"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","The student, Ning Jiang, accepted the attached license on 2025-07-14 at 13:10.","The student, Ning Jiang, submitted this Dissertation for approval on 2025-07-14 at 13:17.","This Dissertation was approved for publication on 2025-07-16 at 15:57.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22502 on 2025-10-20 at 20:15:09","This thesis explores analytic and holomorphic structures in Lie groupoids, Lie algebroids, and Poisson geometry. The first chapter provides background material on Lie groupoids, Lie algebroids, and Poisson structures. In the second chapter, we prove that any analytic s-proper Lie groupoid is analytically linearizable. Our approach relies on constructing an analytic Haar density and an analytic 2-metric on groupoids. The third chapter introduces the notion of complexification for analytic Lie algebroids. We establish that when the anchor map is injective or surjective, the integrability of the original algebroid implies the integrability of its complexification. Moreover, if the analytic algebroid is of s-proper type, its complexification is locally integrable. In the fourth chapter, we develop a computer program for computing the holomorphic Poisson cohomology of projective spaces."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/129932"],"dc:language":["en","eng"],"dc:rights":["Copyright 2025 Ning Jiang"],"dc:subject":["Poisson Geometry","Complex Geometry","Lie Groupoid","Lie Algebroid"],"dc:title":["Analytic and holomorphic structures in Lie groupoids, algebroids, and Poisson geometry"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:06Z"}