More properties of Yetter-Drinfeld modules over quasi-Hopf algebras

2003/11/21 by D. Bulacu, Daniel Bulacu, S. Caenepeel +5
Mathematics · #16W30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16W30

paper · pdf · doi:10.48550/arxiv.math/0311381

22 pages

arxiv created 2003/11/21 · openalex publication_date 2003/11/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize various properties of Yetter-Drinfeld modules over Hopf algebras to quasi-Hopf algebras. The dual of a finite dimensional Yetter-Drinfeld module is again a Yetter-Drinfeld module. The algebra H₀ in the category of Yetter-Drinfeld modules that can be obtained by modifying the multiplication in a proper way is quantum commutative. We give a Structure Theorem for Hopf modules in the category of Yetter-Drinfeld modules, and deduce the existence and uniqueness of integrals from it.

Related

• More properties of Yetter-Drinfeld category over dual quasi-Hopf algebras
• Yetter-Drinfeld categories for quasi-Hopf algebras
• Yetter-Drinfeld algebras over a pairing of multiplier Hopf algebras
• Yetter-Drinfeld modules for weak Hom-Hopf algebras
• Notes on Yetter-Drinfeld algebras over Hopf algebras