Trivializing group actions on braided crossed tensor categories and graded 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...

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...

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 Braided Tensor Categories of Type Bcdimre Tuba And

Braided Near-group Categories

A near-group category is an additively semisimple category with a product such that all but one of the simple objects is invertible. We classify braided structures on near-group categories, and give explicit numerical formulas for their associativity and commutativity morphisms. 1. Results We consider near-group categories; that is, semisimple monoidal categories, whose set of simples consists ...