Braided Tensor Categories of Admissible Modules for Affine Lie Algebras

By T. Creutzig, Yi-Zhi Huang, Jinwei Yang. Communications in Mathematical Physics, 2017

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Using the tensor category theory developed by Lepowsky, Zhang and the second author, we construct a braided tensor category structure with a twist on a semisimple category of modules for an affine Lie algebra at an admissible level. We conjecture that this braided tensor category is rigid and thus is a ribbon category. We also give conjectures on the modularity of this category and on the equivalence with a suitable quantum group tensor category. In the special case that the affine Lie algebra is $${\widehat{\mathfrak{sl}}_2}$$sl^2, we prove the rigidity and modularity conjectures.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/648f089f6a212117a95ac1abc37b81ecba21420c