2020/06/22 by Nathan Geer, Geer, Nathan, Ngoc Phu Ha +4 · 8 citations
Mathematics · #17B37 #57M27 #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #FOS: Mathematics #Geometric Topology (math.GT) #Geometry #Homotopy and Cohomology in Algebraic Topology #Hopf algebra #Invariant (physics) #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum #Quantum Algebra (math.QA) #Quantum group #Quantum mechanics #Ribbon #math.GT #math.QA #msc:17B37 #msc:57M27
paper · pdf · doi:10.48550/arxiv.2006.12050
published in arXiv (Cornell University) (Cornell University) · 54 pages, 42 figures
arxiv created 2020/06/22 · openalex publication_date 2020/06/22 · arxiv updated 2020/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The second author constructed a topological ribbon Hopf algebra from the\nunrolled quantum group associated with the super Lie algebra\n mathfraksl(2|1). We generalize this fact to the context of unrolled\nquantum groups and construct the associated topological ribbon Hopf algebras.\nThen we use such an algebra, the discrete Fourier transforms, a symmetrized\ngraded integral and a modified trace to define a modified graded Hennings\ninvariant. Finally, we use the notion of a modified integral to extend this\ninvariant to empty manifolds and show that it recovers the CGP-invariant.\n