Braided Tensor Categories of Admissible Modules for Affine Lie Algebras

Creutzig T, Huang YZ, Yang J (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Book Volume: 362

Pages Range: 827-854

Journal Issue: 3

DOI: 10.1007/s00220-018-3217-6

Abstract

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.

Involved external institutions

University of Alberta CA Canada (CA) Rutgers, The State University of New Jersey US United States (USA) (US) Yale University US United States (USA) (US)

How to cite

APA:

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

MLA:

Creutzig, Thomas, Yi Zhi Huang, and Jinwei Yang. "Braided Tensor Categories of Admissible Modules for Affine Lie Algebras." Communications in Mathematical Physics 362.3 (2018): 827-854.

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