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(1, 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).
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