Abelianization of groupoids and Lie algebroids

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Xiao, Shuyu

Contributors dc:contributor

• Loja Fernandes, Rui A
• Kerman, Ely
• Pascaleff, James
• Berwick Evans, Daniel

• Abelianization
• Lie Algebroid
• Groupoid
• Diffeology
• Genus-integration

Statement dc:rights

• Copyright 2024 Shuyu Xiao

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/124369

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F124369