Tensor categories arising from the Virasoro algebra

T Creutzig; C Jiang; F Orosz Hunziker; D Ridout; J Yang

Journal article

Tensor categories arising from the Virasoro algebra

T Creutzig, C Jiang, F Orosz Hunziker, D Ridout, J Yang

Advances in Mathematics | Published : 2021

DOI: 10.1016/j.aim.2021.107601

Abstract

We show that there is a braided tensor category structure on the category of C1-cofinite modules for the (universal or simple) Virasoro vertex operator algebras of arbitrary central charge. In the generic case of central charge c=13−6(t+t−1), with t∉Q, we prove semisimplicity, rigidity and non-degeneracy and also compute the fusion rules of this tensor category.

University of Melbourne Researchers

David Ridout Author

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Grants

Awarded by Natural Sciences and Engineering Research Council of Canada

Funding Acknowledgements

We would like to thank Yi-Zhi Huang, Robert McRae and Antun Milas for many useful discussions. We also thank the referee for their valuable comments and suggestions. T.C. is supported by NSERC #RES0020460, C.J. is supported by NSFC grants 11771281 and 11531004, DR's research is supported by the Australian Research Council Discovery Project DP160101520.