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 sl^ 2, we prove the rigidity and modularity conjectures.
CITATION STYLE
Creutzig, T., Huang, Y. Z., & Yang, J. (2018). Braided Tensor Categories of Admissible Modules for Affine Lie Algebras. Communications in Mathematical Physics, 362(3), 827–854. https://doi.org/10.1007/s00220-018-3217-6
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