2004/09/30 by S. Caenepeel, Caenepeel, S., Dingguo Wang +3 · 1 citation
Mathematics · #16W30 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16W30
paper · pdf · doi:10.48550/arxiv.math/0409599
22 pages
openalex publication_date 2004/09/30 · arxiv created 2005/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce Yetter-Drinfeld modules over a weak Hopf algebra H, and show that the category of Yetter-Drinfeld modules is isomorphic to the center of the category of H-modules. The categories of left-left, left-right, right-left and right-right Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Yetter-Drinfeld modules can be viewed as weak Doi-Hopf modules, and, a fortiori, as weak entwined modules. If H is finitely generated and projective, then we introduce the Drinfeld double using duality results between entwining structures and smash product structures, and show that the category of Yetter-Drinfeld modules is isomorphic to the category of modules over the Drinfeld double.