相关论文: Semisimple Hopf algebras of dimension $2q^3$

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 $q$ be a prime number, $k$ an algebraically closed field of characteristic 0, and $H$ a semisimple Hopf algebra of dimension $2q^3$. This paper proves that $H$ is always semisolvable. That is, such Hopf algebras can be obtained by (a…

Let H be a Hopf algebra of dimension pq over an algebraically closed field of characteristic zero, where p, q are odd primes with p < q < 4p+12. We prove that H is semisimple and thus isomorphic to a group algebra, or the dual of a group…

Inspired by the work of Radford, for $H$ an arbitrary quasi-Hopf algebra we describe all the Hopf algebras of dimension $2$ within the braided category of left Yetter-Drinfeld modules over $H$ and determine the biproduct quasi-Hopf algebras…

In this paper we contribute to the classification of Hopf algebras of dimension pq, where p,q are distinct prime numbers. More precisely, we prove that if p and q are odd primes with p<q<2p+3, then any complex Hopf algebra of dimension pq…

Let H be a finite dimensional non-semisimple Hopf algebra over an algebraically closed field k of characteristic 0. If H has no nontrivial skew-primitive elements, we find some bounds for the dimension of H_1, the second term in the…

Let $H$ be a non-semisimple Hopf algebra with antipode $S$ of dimension $pq$ over an algebraically closed field of characteristic 0 where $p \le q$ are odd primes. We prove that $\Tr(S^{2p})=p^2d$ where $d \equiv pq \pmod{4}$. As a…

In this paper we consider some properties of semisimple Hopf algebras of dimension pq where p and q are distinct primes. These properties are useful for classification of such Hopf algebras. In particular, we show that for such a Hopf…

Let $p,q$ be prime numbers with $p>q^3$, and $k$ an algebraically closed field of characteristic 0. In this paper, we obtain the structure theorems for semisimple Hopf algebras of dimension $pq^3$.

Let H be a Hopf algebra of dimension pq over an algebraically closed field of characteristic 0, where p <= q are odd primes. Suppose that S is the antipode of H. If H is not semisimple, then S^{4p}=id_H and Tr(S^{2p}) is an integer…

Let $H$ be a finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0. If $H$ is not semisimple and $\dim(H)=2n$ for some odd integer $n$, then $H$ or $H^*$ is not unimodular. Using this result, we prove that…

Let $k$ be an algebraically closed field of characteristic $0$. In this paper, we obtain the structure theorems for semisimple Hopf algebras of dimension $p^2q^2$ over $k$, where $p,q$ are prime numbers with $p^2<q$. As an application, we…

Masuoka proved that for a prime p, semisimple Hopf algebras of dimension 2p over an algebraically closed field k of characteristic 0, are trivial (i.e. are either group algebras or the dual of group algebras). Westreich and the second…

The goal of this paper is to give a new method of constructing finite-dimensional semisimple triangular Hopf algebras, including minimal ones which are non-trivial (i.e. not group algebras). The paper shows that such Hopf algebras are quite…

Let H be a cosemisimple Hopf algebra over an algebraically closed field k which contains a simple subcoalgebra of dimension 9. We show that if H has no simple subcoalgebras of even dimension then H contains either a grouplike element with…

Let H be a non-semisimple Hopf algebra of dimension 2p^2 over an algebraically closed field of characteristic zero, where p is an odd prime. We prove that H or H^* is pointed, which completes the classification for Hopf algebras of these…

Let p and q be distinct odd primes and assume k is an algebraically closed field of characteristic zero. We classify all quasitriangular Hopf algebras of dimension pq^2 over k, which are not simple as Hopf algebras. Moreover, we obtained…

In this paper, we prove that a non-semisimple Hopf algebra H of dimension 4p with p an odd prime over an algebraically closed field of characteristic zero is pointed provided H contains more than two group-like elements. In particular, we…

We prove a structure theorem for Yetter-Drinfel'd Hopf algebras over groups of prime order that are nontrivial, cocommutative, and cosemisimple: Under certain assumptions on the base field, these algebras can be decomposed into a tensor…

Let $k$ be an algebraically closed field of characteristic 0. In this paper, we obtain the structure theorems for semisimple Hopf algebras of dimension $9q^2$ over $k$, where $q$ is a prime number. We also prove that odd-dimensional…