2009/07/13 by Seung-Moon Hong, Hong, Seung-Moon · 2 citations
Mathematics · #57M27 #57R56 #81P68 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.0907.2204
openalex publication_date 2009/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that every ribbon category with unimodality allows symmetrized 6j-symbols with full tetrahedral symmetries while a spherical category does not in general. We give an explicit counterexample for this, namely the category E. We define the mirror conjugate symmetry of 6j-symbols instead and show that 6j-symbols of any unitary spherical category can be normalized to have this property. As an application, we discuss an exactly soluble model on a honeycomb lattice. We prove that the Levin-Wen Hamiltonian is exactly soluble and hermitian on a unitary spherical category.