Direct limit completions of vertex tensor categories

Thomas Creutzig University of Alberta Robert McRae Tsinghua University Jinwei Yang University of Alberta

Category Theory Mathematical Physics Quantum Algebra Representation Theory mathscidoc:2204.04005

Communications in Contemporary Mathematics, 24, (2), 2150033, 2022.3
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 osp(1|2) and the N=1 super Virasoro algebra to categories of Virasoro algebra modules via certain cosets.
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@inproceedings{thomas2022direct,
  title={Direct limit completions of vertex tensor categories},
  author={Thomas Creutzig, Robert McRae, and Jinwei Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220415172243262679053},
  booktitle={Communications in Contemporary Mathematics},
  volume={24},
  number={2},
  pages={2150033},
  year={2022},
}
Thomas Creutzig, Robert McRae, and Jinwei Yang. Direct limit completions of vertex tensor categories. 2022. Vol. 24. In Communications in Contemporary Mathematics. pp.2150033. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220415172243262679053.
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