相关论文: Unbraiding the braided tensor product

We briefly report on our result that the braided tensor product algebra of two module algebras $A_1,A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $H_1$ with a subalgebra isomorphic to $A_2$…

We briefly review and illustrate our procedure to 'decouple' by transformation of generators: either a Hopf algebra $H$ from a $H$-module algebra $A_1$ in their cross-product $A_1 >\triangleleft H$; or two (or more) $H$-module algebras…

We show how to define the tensor product of two braided Hopf algebras.

We show that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then one can split their cross-product into the tensor product algebra of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$.…

A known fundamental Theorem for braided pointed Hopf algebras states that for each coideal subalgebra, that fulfils a few properties, there is an associated quotient coalgebra right module such that the braided Hopf algebra can be…

We show that the algebra of the bicovariant differential calculus on a quantum group can be understood as a projection of the cross product between a braided Hopf algebra and the quantum double of the quantum group. The resulting super-Hopf…

We prove the graded braided commutativity of the Hochschild cohomology of $A$ with trivial coefficients, where $A$ is a braided Hopf algebra in the category of Yetter-Drinfeld modules over the group algebra of an abelian group, under some…

The main properties of the crossed product in the category of Hopf algebras are investigated. Let $A$ and $H$ be two Hopf algebras connected by two morphism of coalgebras $\triangleright : H\ot A \to A$, $f:H\ot H\to A$. The crossed product…

We classify braided tensor categories over C of exponential growth which are quasisymmetric, i.e., the squared braiding is the identity on the product of any two simple objects. This generalizes the classification results of Deligne on…

Based on a pairing of two regular multiplier Hopf algebras $A$ and $B$, Heisenberg double $\mathscr{H}$ is the smash product $A \# B$ with respect to the left regular action of $B$ on $A$. Let $\mathscr{D}=A\bowtie B$ be the Drinfel'd…

We apply Majid's transmutation procedure to Hopf algebra maps $H \to \mathbb C[T]$, where $T$ is a compact abelian group, and explain how this construction gives rise to braided Hopf algebras over quotients of $T$ by subgroups that are…

We give a review and some new relations on the structure of the monodromy algebra (also called loop algebra) associated with a quasitriangular Hopf algebra H. It is shown that as an algebra it coincides with the so-called braided group…

We introduce a definition of braided tensor product $\operatorname{M}\overline{\boxtimes}\operatorname{N}$ of von Neumann algebras equipped with an action of a quasi-triangular quantum group $\mathbb{G}$ (this includes the case when…

We construct the join of noncommutative Galois objects (quantum torsors) over a Hopf algebra H. To ensure that the join algebra enjoys the natural (diagonal) coaction of H, we braid the tensor product of the Galois objects. Then we show…

Let k be a field. Let also (F, G) be a matched pair of groups. We give necessary and sufficient conditions on a pair (\sigma, \tau) of 2-cocycles in order that the crossed product algebra and the crossed coproduct coalgebra…

We use the theory of regular objects in tensor categories to clarify the passage between braided multiplicative unitaries and multiplicative unitaries with projection. The braided multiplicative unitary and its semidirect product…

Let $(H,R)$ be a quasitriangular weak Hopf algebra over a field $k$. We show that there is a braided monoidal equivalence between the Yetter-Drinfeld module category $^H_H\mathscr{YD}$ over $H$ and the category of comodules over some…

With the motivation of giving a more precise estimation of the quantum Brauer group of a Hopf algebra $H$ over a field $k$ we construct an exact sequence containing the quantum Brauer group of a Hopf algebra in a certain braided monoidal…

We briefly report on our result that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then their cross-product is equal to the product of $A$ itself with a subalgebra isomorphic to $H$ and commuting with…

Hilbert space representations of the cross product *-algebras of the Hopf *-algebra U_q(su_2) and its module *-algebras O(S^2_{qr}) of Podles spheres are investigated and classified by describing the action of generators. The…