Direct limit completions of vertex tensor categories
Thomas Creutzig, Robert McRae, Jinwei Yang
Abstract
We show that direct limit completions of vertex tensor categories inherit vertex and braided tensor category structures, under conditions that hold for example for all known Virasoro and affine Lie algebra tensor categories. A consequence is that the theory of vertex operator (super)algebra extensions also applies to infinite-order extensions. As an application, we relate rigid and non-degenerate vertex tensor categories of certain modules for both the affine vertex superalgebra of [Formula: see text] and the [Formula: see text] super Virasoro algebra to categories of Virasoro algebra modules via certain cosets.
Topics & Concepts
MathematicsVertex (graph theory)Vertex operator algebraPure mathematicsSuperalgebraVirasoro algebraLie superalgebraAffine transformationTensor (intrinsic definition)Affine Lie algebraLie conformal algebraTensor productAlgebra over a fieldVertex modelCurrent algebraTensor contractionLimit (mathematics)Direct limitTensor product of modulesTensor product of algebrasOperator algebraSymmetric tensorQuantum affine algebraGraded Lie algebraLie algebraTensor fieldRepresentation theoryOperator product expansionAlgebraic structures and combinatorial modelsHomotopy and Cohomology in Algebraic TopologyFinite Group Theory Research