Invertible braided tensor categories

On Braided Tensor Categories of Type Bcd

We give a full classification of all braided semisimple tensor categories whose Grothendieck semiring is the one of Rep ( O(∞) ) (formally), Rep ( O(N) ) , Rep ( Sp(N) ) , or of one of its associated fusion categories. If the braiding is not symmetric, they are completely determined by the eigenvalues of a certain braiding morphism, and we determine precisely which values can occur in the vario...

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...

On Algebraic Construction in Braided Tensor Categories

Braided Hopf algebras have attracted much attention in both mathematics and mathematical physics (see e.g. [1][4][13][15][17][16][20][23]). The classification of finite dimensional Hopf algebras is interesting and important for their applications (see [2] [22]). Braided Hopf algebras play an important role in the classification of finite-dimensional pointed Hopf algebras (e.g. [2][1] [19]). The...

Representations of vertex operator algebras and braided finite tensor categories

We discuss what has been achieved in the past twenty years on the construction and study of a braided finite tensor category structure on a suitable module category for a suitable vertex operator algebra. We identify the main difficult parts in the construction, discuss the methods developed to overcome these difficulties and present some further problems that still need to be solved. We also c...

Algebra in Braided Tensor Categories and Conformal Field Theory