2022/04/06 by Kazuo Habiro, Habiro, Kazuo, Yuka Kotorii +1
Mathematics · #16T05 #18M15 #57K10 #57K16 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2204.02551
openalex publication_date 2022/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define notions of pivotal and ribbon objects in a monoidal category. These constructions give pivotal or ribbon monoidal categories from a monoidal category which is not necessarily with duals. We apply this construction to the braided monoidal category of Yetter--Drinfeld modules over a Hopf algebra. This gives rise to the notion of ribbon Yetter--Drinfeld modules over a Hopf algebra, which form ribbon categories. This gives an invariant of tangles.