• DOI:10.1081/AGB-200065383
• Corpus ID: 58913879

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, of D(An(ω)) for any n ≥ 2. We investigate the indecomposable left Hn(1, q)-module, and describe the structures and properties of all indecomposable modules and classify them when k is algebraically closed. We also give all almost split sequences in mod Hn(1, q), and the Auslander-Reiten-quiver of Hn(1 q).