Generic Modules Over a Class of Drinfeld's Quantum Doubles
Titel:
Generic Modules Over a Class of Drinfeld's Quantum Doubles
Auteur:
Wang, Zhen Chen, Hui-Xiang
Verschenen in:
Communications in algebra
Paginering:
Jaargang 36 (2008) nr. 10 pagina's 3730-3749
Jaar:
2008-10
Inhoud:
Let k be a field and An(ω) be the Taft's n2-dimensional Hopf algebras. 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 finite dimensional representations of Hn(1, q). We showed that the basic algebra of any nonsimple block of Hn(1, q) is independent of n. In this article, we examine the infinite representations of H2(1, - 1), or equivalently of Hn(1, q)≃D(An(ω)) for any n ≥ 2. We investigate the indecomposable and algebraically compact modules over H2(1, - 1), describe the structures of these modules and classify them under the elementary equivalence.
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