University of Illinois Urbana-Champaign

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

Nguyen, Anh Tuong

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

Description

Title
Coend elements of a Hopf algebra in a braided rigid monoidal category
Author(s)
Nguyen, Anh Tuong
Issue Date
2024-04-29
Director of Research (if dissertation) or Advisor (if thesis)
Walton, Chelsea
Doctoral Committee Chair(s)
Dodd, Christopher
Committee Member(s)
  • Rezk, Charles
  • Berwick-Evans, Daniel
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • braided Hopf algebra
  • coend
  • modular tensor category
  • pivotal element
  • ribbon element
Abstract
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.
Graduation Semester
2024-05
Type of Resource
Thesis
Copyright and License Information
Copyright 2024 Anh Tuong Nguyen

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