Determinants and symmetries in 'Yetter-Drinfeld' categories

Miriam Cohen, Sara Westreich

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

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
Volume6
Issue number2
DOIs
StatePublished - 1 Jan 1998

Keywords

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

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