2026-09-22T10:43:44Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/124369 2024-09-16 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Loja Fernandes, Rui A Kerman, Ely Pascaleff, James Berwick Evans, Daniel 2024-05 application/pdf en text 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 Abelianization of groupoids and Lie algebroids Xiao, Shuyu 2024-04-24 Abelianization Lie Algebroid Groupoid Diffeology Genus-integration 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. Text eng https://hdl.handle.net/2142/124369 Copyright 2024 Shuyu Xiao Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics