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Finite-Dimensional Representations of a Quantum Double

✍ Scribed by Hui-Xiang Chen

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
269 KB
Volume
251
Category
Article
ISSN
0021-8693

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✦ Synopsis

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 .  2002 Elsevier Science (USA)

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