On Ribbon Categories for Singlet Vertex Algebras - Creutzig, Thomas; McRae, Robert; Yang, Jinwei (Communications in Mathematical Physics, 2021)
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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