• DOI:10.1006/JABR.2002.9144
• Corpus ID: 122996184

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}
}

• Hui-xiang Chen
• Published 15 May 2002
• Mathematics
• Journal of Algebra

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 ), equivalently, of D ( A 3 (ω)). We investigate the indecomposable left H 3 (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  H 3 (1,  q ), and the Auslander–Reiten quiver of H 3 (1,  q ).