On Braided Tensor Categories of Type Bcd

On a Family of Non-unitarizable Ribbon Categories

We consider several families of categories. The first are quotients of Andersen’s tilting module categories for quantum groups of Lie type B at odd roots of unity. The second consists of categories of type BC constructed from idempotents in BMW -algebras. Our main result is to show that these families coincide as braided tensor categories using a recent theorem of Tuba and Wenzl. By appealing t...

On Braided Tensor Categories of Type Bcdimre Tuba And

Hopf Galois Extension in Braided Tensor Categories

The relation between crossed product and H-Galois extension in braided tensor categories is established. It is shown that A = B#σH is a crossed product algebra if and only if the extension A/B is Galois, the inverse can of the canonical morphism can factors through object A⊗B A and A is isomorphic as left B-modules and right H-comodules to B⊗H in braided tensor categories. For the Yetter-Drinfe...

Tensor categories and the mathematics of rational and logarithmic conformal field theory

We review the construction of braided tensor categories and modular tensor categories from representations of vertex operator algebras, which correspond to chiral algebras in physics. The extensive and general theory underlying this construction also establishes the operator product expansion for intertwining operators, which correspond to chiral vertex operators, and more generally, it establi...

On the Braiding on a Hopf Algebra in a Braided Category

By definition, a bialgebra H in a braided monoidal category (C, τ) is an algebra and coalgebra whose multiplication and comultiplication (and unit and counit) are compatible; the compatibility condition involves the braiding τ . The present paper is based upon the following simple observation: If H is a Hopf algebra, that is, if an antipode exists, then the compatibility condition of a bialgebr...