# REPRESENTATIONS OF A CLASS OF DRINFELD'S DOUBLES

@article{Chen2005REPRESENTATIONSOA, title={REPRESENTATIONS OF A CLASS OF DRINFELD'S DOUBLES}, author={Hui-xiang Chen}, journal={Communications in Algebra}, year={2005}, volume={33}, pages={2809 - 2825} }

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 an n4-dimensional Hopf algebra Hn(p, q) which is isomorphic to D(An(ω)) if p ≠ 0 and q = ω−1 , and studied the irreducible representations of Hn(1, q) and the finite dimensional representations of H3(1, q). In this article, we examine the finite-dimensional representations of Hn(l q), equivalently…

## 16 Citations

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

- Mathematics
- 2008

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…

### Grothendieck Groups of a Class of Quantum Doubles

- Mathematics
- 2008

Let k be a field and An(ω) be the Taft n2-dimensional Hopf algebra. When n is odd, the Drinfeld quantum double D(An(ω)) of An(ω) is a ribbon Hopf algebra. We have constructed an n4-dimensional Hopf…

### The Cell Modules of the Green Algebra of Drinfel’d Quantum Double D(H4)

- MathematicsActa Mathematica Sinica, English Series
- 2022

This paper is devoted to studying the structures of the cell modules of the complexified Green algebra R(D(H4)), where D(H4) is the Drinfel’d quantum double of Sweedler’s 4-dimensional Hopf algebra…

### The Green Ring of Drinfeld Double D(H4)

- Mathematics
- 2014

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…

### The Projective Class Rings of a family of pointed Hopf algebras of Rank two

- Mathematics
- 2016

In this paper, we compute the projective class rings of the tensor product $\mathcal{H}_n(q)=A_n(q)\otimes A_n(q^{-1})$ of Taft algebras $A_n(q)$ and $A_n(q^{-1})$, and its cocycle deformations…

### The Green ring of a family of copointed Hopf algebras

- Mathematics
- 2022

The copointed liftings of the Fomin-Kirillov algebra $\mathcal{FK}_3$ over the algebra of functions on the symmetric group $\mathbb{S}_3$ were classified by Andruskiewitsch and the author. We…

### McKay matrix for indecomposable module of finite representation type Hopf algebra

- MathematicsCommunications in Algebra
- 2022

Abstract Let H be a Hopf algebra of finite representation type. For the grouplike elements and skew-primitive elements in H, we prove some general results about the eigenvalues and eigenvectors of…

### Green rings of Drinfeld doubles of Taft algebras

- MathematicsCommunications in Algebra
- 2020

Abstract In this article, we investigate the representation rings (or Green rings) of the Drinfeld doubles of the Taft algebras. It is shown that these Green rings are commutative rings generated by…

## References

SHOWING 1-10 OF 19 REFERENCES

### Finite-Dimensional Representations of a Quantum Double

- Mathematics
- 2002

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…

### Representations of Finite-Dimensional Hopf Algebras

- Mathematics
- 1997

Abstract LetHdenote a finite-dimensional Hopf algebra with antipodeSover a field k . We give a new proof of the fact, due to OS , thatHis a symmetric algebra if and only ifHis unimodular andS2is…

### Algebraic K-theory

- Mathematics
- 2005

The idea will be to associate to a ring R a set of algebraic invariants, Ki(R), called the K-groups of R. We can even do a little better than that: we will associated an (infinite loop) space K(R) to…

### Über Untergruppen Endlicher Algebraischer Gruppen

- Mathematics
- 1973

Let k be a commutative ring, G′⊃G finite affine algebraic k-groups, and H′⊃H the dual Hopfalgebras of the affine algebras of G′ resp. G. The main results of this paper are: (I) If k is semilocal…

### An Introduction to Homological Algebra

- Mathematics
- 1979

An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext…

### The Order of the Antipode of Finite-dimensional Hopf Algebra.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1971

Examples of finite-dimensional Hopf algebras over a field, whose antipodes have arbitrary even orders >/=4 as mappings, are furnished. The dimension of the Hopf algebra is q(n+1), where the antipode…

### Quantum Groups

- Mathematics
- 1994

Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups…

### Foundations of Quantum Group Theory

- Mathematics
- 1995

Introduction 1. Definition of Hopf algebras 2. Quasitriangular Hopf algebras 3. Quantum enveloping algebras 4. Matrix quantum groups 5. Quantum random walks and combinatorics 6. Bicrossproduct Hopf…

### Representation Theory of Artin Algebras: Contents

- Mathematics
- 1995

1. Artin rings 2. Artin algebras 3. Examples of algebras and modules 4. The transpose and the dual 5. Almost split sequences 6. Finite representation type 7. The Auslander-Reiten-quiver 8. Hereditary…