2026-09-22T03:15:15Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/124587 2026-01-14 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Walton, Chelsea Dodd, Christopher Rezk, Charles Berwick-Evans, Daniel 2024-05 application/pdf en text Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-05-01 The student, Anh Tuong Nguyen, accepted the attached license on 2024-04-26 at 13:24. The student, Anh Tuong Nguyen, submitted this Dissertation for approval on 2024-04-26 at 14:04. This Dissertation was approved for publication on 2024-04-29 at 13:10. DSpace SAF Submission Ingestion Package generated from Vireo submission #20659 on 2024-09-16 at 00:44:48 Coend elements of a Hopf algebra in a braided rigid monoidal category Nguyen, Anh Tuong 2024-04-29 Braided Hopf Algebra Coend Modular Tensor Category Pivotal Element Ribbon Element 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. Text eng https://hdl.handle.net/2142/124587 Copyright 2024 Anh Tuong Nguyen Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics