相关论文: Integrals of Braided Hopf Algebras

In this paper we introduce the category of strong Hopf modules for a weak Hopf quasigroup H in a braided monoidal category. We also prove that this category is equivalent to the category of right modules over the image of the target…

A quasi-Hopf algebra $H$ can be seen as a commutative algebra $A$ in the centre $\mathcal Z(H-Mod)$ of $H-Mod$. We show that the category of $A$-modules in $\mathcal Z(H-Mod)$ is equivalent (as a monoidal category) to $H-Mod$. This can be…

Let $D(H)$ be the quantum double associated to a finite dimensional quasi-Hopf algebra $H$. In this note, we first generalize a result of Majid, stating that a finite dimensional Hopf algebra $H$ is quasitriangular if and only if there is a…

Let $(H, \a)$ be a monoidal Hom-Hopf algebra and $(A, \b)$ a right $(H, \a)$-Hom-comodule algebra. We first investigate the criterion for the existence of a total integral of $(A, \b)$ in the setting of monoidal Hom-Hopf algebras. Also we…

We introduce Yetter-Drinfeld modules over a weak Hopf algebra $H$, and show that the category of Yetter-Drinfeld modules is isomorphic to the center of the category of $H$-modules. The categories of left-left, left-right, right-left and…

In a previous work \cite{AS2} we showed how to attach to a pointed Hopf algebra A with coradical $\k\Gamma$, a braided strictly graded Hopf algebra R in the category $_{\Gamma}^{\Gamma}\Cal{YD}$ of Yetter-Drinfeld modules over $\Gamma$. In…

We study super-braided Hopf algebras $\Lambda$ primitively generated by finite-dimensional right crossed (or Drinfeld-Radford-Yetter) modules $\Lambda^1$ over a Hopf algebra $A$ which are quotients of the augmentation ideal $A^+$ under…

We show that an $L_\infty$-algebra can be extended to a graded Hopf algebra with a codifferential. Then we twist this extended $L_\infty$-algebra with a Drinfel'd twist, simultaneously twisting its modules. Taking the $L_\infty$-algebra as…

We introduce the notion of iHopf algebra, a new associative algebra structure defined on a Hopf algebra equipped with a Hopf pairing. The iHopf algebra on a Borel quantum group endowed with a $\tau$-twisted Hopf pairing is shown to be a…

We compute the representation-theoretic rank of a finite dimensional quasi-Hopf algebra $H$ and of its quantum double $D(H)$, within the rigid braided category of finite dimensional left $D(H)$-modules.

The natural problem we approach in the present paper is to show how the notion of formally smooth (co)algebra inside monoidal categories can substitute that of (co)separable (co)algebra in the study of splitting bialgebra homomorphisms.…

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 $A_2$…

It is proved in this paper that for any finite-dimensional nonsemisimple Hopf algebra $A$ there exists a Hopf algebra $H$ containing $A$ as a Hopf subalgebra such that $H$ is not flat over $A$. On the other hand, there is a class of…

We show that for a braided Hopf algebra in the category of comodules over a cosemisimple coquasitriangular Hopf algebra, the Hochschild cohomological dimension, the left and right global dimensions and the projective dimensions of the…

Rational Hopf algebras (certain quasitriangular weak quasi-Hopf $^*$-algebras) are expected to describe the quantum symmetry of rational field theories. In this paper methods are developped which allow for a classification of all rational…

Let $(H,\alpha)$ be a monoidal Hom-Hopf algebra and $^{H}_{H}\mathcal{HYD}$ the Hom-Yetter-Drinfeld category over $(H,\alpha)$. Then in this paper, we first introduce the definition of braided Hom-Lie algebras and show that each monoidal…

Starting with a self-dual Hopf algebra H in a braided monoidal category S we construct a Z/2Z-graded monoidal category C = C_0 + C_1. The degree zero component is the category Rep_S(H) of representations of H and the degree one component is…

We show that the braided Hochschild cohomology, of an algebra in a suitably algebraic braided monoidal category, admits a graded ring structure under which it is braided commutative. We then give a canonical identification between the usual…

It is shown in math.QA/0301027 that a finite dimensional quasi-Hopf algebra with radical of codimension 1 is semisimple and 1-dimensional. On the other hand, there exist quasi-Hopf (in fact, Hopf) algebras, whose radical has codimension 2.…

We study the Nichols algebra of a semisimple Yetter-Drinfeld module and introduce new invariants such as real roots. The crucial ingredient is a `reflection' in the class of such Nichols algebras. We conclude the classifications of…