Braided Tensor Categories Related to B-p Vertex Algebras

摘要

The B-p-algebras are a family of vertex operator algebras parameterized by p is an element of 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 beta gamma vertex operator algebra. We study categories related to the B-p 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.