Tetrahedral symmetry of 6j-symbols in fusion categories
Jürgen Fuchs, Tobias Grøsfjeld
Abstract
We establish tetrahedral symmetries of 6j-symbols for arbitrary fusion categories under minimal assumptions. As a convenient tool for our calculations we introduce the notion of a veined fusion category, which is generated by a finite set of simple objects but is larger than its skeleton. Every fusion category C contains veined fusion subcategories that are monoidally equivalent to C and which suffice to compute many categorical properties for C. The notion of a veined fusion category does not assume the presence of a pivotal structure, and thus in particular does not assume unitarity. We also exhibit the geometric origin of the algebraic statements for the 6j-symbols.
Topics & Concepts
FusionMathematicsSimple (philosophy)Categorical variableSymmetry (geometry)Set (abstract data type)TetrahedronPure mathematicsFusion rulesAlgebraic numberHomogeneous spaceAlgebra over a fieldComputer scienceImage fusionGeometryMathematical analysisProgramming languageStatisticsPhilosophyLinguisticsEpistemologyAlgebraic structures and combinatorial modelsAdvanced Algebra and GeometryHomotopy and Cohomology in Algebraic Topology