# 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}
}
• Hui-xiang Chen
• Published 1 July 2005
• Mathematics
• Communications in Algebra
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…
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## References

SHOWING 1-10 OF 19 REFERENCES

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
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
• 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
• 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 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
• E. Taft
• Mathematics
Proceedings 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
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
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
• 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