On ribbon categories for singlet vertex algebras

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

Category Theory Mathematical Physics Quantum Algebra Representation Theory mathscidoc:2204.04006

Communications in Mathematical Physics, 387, (2), 865-925, 2021.10
We construct two non-semisimple braided ribbon tensor categories of modules for each singlet vertex operator algebra M(p), p≥2. The first category consists of all finite-length M(p)-modules with atypical composition factors, while the second is the subcategory of modules that induce to local modules for the triplet vertex operator algebra W(p). We show that every irreducible module has a projective cover in the second of these categories, although not in the first, and we compute all fusion products involving atypical irreducible modules and their projective covers.
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  title={On ribbon categories for singlet vertex algebras},
  author={Thomas Creutzig, Robert McRae, and Jinwei Yang},
  booktitle={Communications in Mathematical Physics},
Thomas Creutzig, Robert McRae, and Jinwei Yang. On ribbon categories for singlet vertex algebras. 2021. Vol. 387. In Communications in Mathematical Physics. pp.865-925. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220415172804126105054.
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