Determinants and symmetries in 'Yetter-Drinfeld' categories

Miriam Cohen, Sara Westreich

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


A Yetter-Drinfeld category over a Hopf algebra H with a bijective antipode, is equipped with a 'braiding' which may be symmetric for some of its subcategories (e.g. when H is a triangular Hopf algebra). We prove that under an additional condition (which we term the u-condition) such symmetric subcategories completely resemble the category of vector spaces over a field k, with the ordinary 'flip' map. Consequently, when Char k = 0, one can define well behaving exterior algebras and non-commutative determinant functions.

Original languageEnglish
Pages (from-to)267-289
Number of pages23
JournalApplied Categorical Structures
Issue number2
StatePublished - Jun 1998

Bibliographical note

Funding Information:
★ This research was supported by THE ISRAEL SCIENCE FOUNDATION founded by the Israel Academy of Sciences and Humanities.


  • Braided monoidal category
  • Characters
  • Symmetric category
  • The u-condition
  • Yetter-Drinfeld category


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