Braided Tensor Categories Related to Bp Vertex Algebras - Auger, Jean; Creutzig, Thomas; Kanade, Shashank; Rupert, Matthew (Communications in Mathematical Physics, 2020)
The Bp-algebras are a family of vertex operator algebras parameterized by p∈ Z≥ 2. They are important examples of logarithmic CFTs and appear as chiral algebras of type (A1, A2p-3) Argyres–Douglas theories. The first member of this series, the B2-algebra, are the well-known symplectic bosons also often called the βγ vertex operator algebra. We study categories related to the Bp vertex operator algebras using their conjectural relation to unrolled restricted quantum groups of sl2. These categories are braided, rigid and non semi-simple tensor categories. We list their simple and projective objects, their tensor products and their Hopf links. The latter are succesfully compared to modular data of characters thus confirming a proposed Verlinde formula of David Ridout and the second author.
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