# Finite-Dimensional Representations of a Quantum Double

@article{Chen2002FiniteDimensionalRO, title={Finite-Dimensional Representations of a Quantum Double}, author={Hui-xiang Chen}, journal={Journal of Algebra}, year={2002}, volume={251}, pages={751-789} }

Abstract Let k be a field and let A n (ω) be the Taft's n 2 -dimensional Hopf algebra. When n is odd, the Drinfeld quantum double D ( A n (ω)) of A n (ω) is a ribbon Hopf algebra. In a previous paper we constructed an n 4 -dimensional Hopf algebra H n ( p , q ) which is isomorphic to D ( A n (ω)) if p ≠ 0 and q = ω − 1 , and studied the irreducible representations of H n (1, q ). We continue our study of H n ( p , q ), and we examine the finite-dimensional representations of H 3 (1, q…

## 25 Citations

### Generic Modules Over a Class of Drinfeld's Quantum Doubles

- Mathematics
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Let k be a field and A n (ω) be the Taft's n 2-dimensional Hopf algebras. When n is odd, the Drinfeld quantum double D(A n (ω)) of A n (ω) is a Ribbon Hopf algebra. In the previous articles, we…

### REPRESENTATIONS OF A CLASS OF DRINFELD'S DOUBLES

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Let k be a field and An(ω) be the Taft's n2-dimensional Hopf algebra. When n is odd, the Drinfeld quantum double D(An(ω)) of An(ω) is a ribbon Hopf algebra. In the previous articles, we constructed…

### Grothendieck Groups of a Class of Quantum Doubles

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Let Uq(sl2) be the quantized enveloping algebra associated to the simple Lie algebra sl2. In this paper, we study the quantum double Dq of the Borel subalgebra Uq((sl2) ) of Uq(sl2). We construct an…

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In this paper, we study the representation theory of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one over an arbitrary field k. Let H=kG(χ,a,δ) be a Hopf-Ore extension of…

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- MathematicsAlgebras and Representation Theory
- 2015

In this paper, we study the representation theory of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one over an arbitrary field k. Let H=kG(χ,a,δ) be a Hopf-Ore extension of…

### The Green rings of Taft algebras

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We compute the Green ring of the Taft algebra $H_n(q)$, where $n$ is a positive integer greater than 1, and $q$ is an $n$-th root of unity. It turns out that the Green ring $r(H_n(q))$ of the Taft…

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In this paper, we study the Green ring (or the representation ring) of Drinfeld quantum double D(H4) of Sweedler’s four-dimensional Hopf algebra H4. We first give the decompositions of the tensor…

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