Related papers: Semisimple Hopf actions on commutative domains

Let $\left( H,R\right) $ be a finite dimensional semisimple and cosemisimple quasi-triangular Hopf algebra over a field $k$. In this paper, we give the structure of irreducible objects of the Yetter-Drinfeld module category ${}…

We show that the invariants of a free associative algebra of finite rank under a linear action of a finite-dimensional Hopf algebra generated by group-like and skew-primitive elements form a finitely generated algebra exactly when the…

In this note we prove a generalization of the Frobenius-Schur theorem for finite groups for the case of semisimple Hopf algebra over an algebraically closed field of characteristic 0. A similar result holds in characteristic $p > 2$ if the…

We introduce a Hopf algebroid associated to a proper Lie group action on a smooth manifold. We prove that the cyclic cohomology of this Hopf algebroid is equal to the de Rham cohomology of invariant differential forms. When the action is…

Using the standard filtration associated with a generalized lifting method, we determine all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose coradical generates a Hopf subalgebra isomorphic…

We prove that the kernel of the natural action of the modular group on the center of the Drinfel'd double of a semisimple Hopf algebra is a congruence subgroup. To do this, we introduce a class of generalized Frobenius-Schur indicators and…

Let $p,q$ be prime numbers with $p^4<q$, and $k$ an algebraically closed field of characteristic 0. We show that semisimple Hopf algebras of dimension $p^2q^2$ can be constructed either from group algebras and their duals by means of…

Let $H$ and $L$ be quantum groupoids. If $H$ has a quasitriangular structure, then we show that $L$ induces a Hopf algebra $C_{L}(L_s)$ in the category $_{H}\mathcal{M}$, which generalizes the transmutation theory introduced by Majid.…

For each nontrivial semisimple Hopf algebra $H$ of dimension sixteen over $\mathbb{C}$, the smallest dimension inner-faithful representation of $H$ acting on a quadratic AS regular algebra $A$ of dimension 2 or 3, homogeneously and…

Kaplansky conjectured that if H is a finite-dimensional semisimple Hopf algebra over an algebraically closed field k of characteristic 0, then H is of Frobenius type (i.e. if V is an irreducible representation of H then dimV divides dimH).…

We develop a mechanism for classication of isomorphism types of non-trivial semisimple Hopf algebras whose group of grouplikes $G(H)$ is abelian of prime index $p$ which is the smallest prime divisor of $|G(H)|$. We describe structure of…

Given a locally finite graded set A and a commutative, associative operation on A that adds degrees, we construct a commutative multiplication * on the set of noncommutative polynomials in A which we call a quasi-shuffle product; it can be…

If H is a quasi-Hopf algebra and B is a right H-comodule algebra such that there exists v:H\to B a morphism of right H-comodule algebras, we prove that there exists a left H-module algebra A such that B\simeq A# H. The main difference…

We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We…

We show that the main results of Happel-Rickard-Schofield (1988) and Happel-Reiten-Smalo (1996) on piecewise hereditary algebras are coherent with the notion of group action on an algebra. Then, we take advantage of this compatibility and…

We establish a bijective correspondence between gauge equivalence classes of dynamical twists in a finite-dimensional Hopf algebra $H$ based on a finite abelian group $A$ and equivalence classes of pairs $(K, \{V_{\lambda}\}_{\lambda\in…

We try to classify Hopf algebras with the dual Chevalley property of discrete corepresentation type over an algebraically closed field $\Bbb{k}$ with characteristic 0. For such Hopf algebra $H$, we characterize the link quiver of $H$ and…

Any finite-dimensional quasitriangular Hopf algebra $H$ can be formally extended to a ribbon Hopf algebra $\tilde H$ of twice the dimension. We investigate this extension and its representations. We show that every indecomposable $H$-module…

In a previous paper we prove that any semisimple triangular Hopf algebra A over an algebraically closed field of characteristic 0 (say the field of complex numbers C) is obtained from a finite group after twisting the ordinary…

We derive necessary and sufficient conditions for an ambiskew polynomial ring to have a Hopf algebra structure of a certain type. This construction generalizes many known Hopf algebras, for example U(sl2), U_q(sl2) and the enveloping…