Coend elements of a Hopf algebra in a braided rigid monoidal category

Let H be a Hopf algebra in a braided rigid monoidal category V admitting a coend C. We define a “coend element” of H to be a morphism from C to H. We then study certain coend elements of H, which generalize important elements (e.g., pivotal and ribbon elements) of a finite dimensional Hopf algebra over a field. This builds on prior work of Bruguieres and Virelizier on elements of Hopf monads and R-matrices of braided Hopf algebras. As a consequence, we provide another description for pivotal and ribbon structures on the category of H-modules.

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

• Nguyen, Anh Tuong

Contributors dc:contributor

• Walton, Chelsea
• Dodd, Christopher
• Rezk, Charles
• Berwick-Evans, Daniel

• Braided Hopf Algebra
• Coend
• Modular Tensor Category
• Pivotal Element
• Ribbon Element

Statement dc:rights

• Copyright 2024 Anh Tuong Nguyen

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/124587

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F124587