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Representations of pointed Hopf algebras and their Drinfel'd quantum doubles |
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| Authors: | Leonid Krop David E. Radford |
| Affiliation: | 1. DePaul University, Department of Mathematical Sciences, 2320 N. Kenmore, Chicago, IL 60614, United States;2. University of Illinois at Chicago, Department of Mathematics, Statistics and Computer Science, 801 South Morgan Street, Chicago, IL 60607-7045, United States |
| Abstract: | We study representations of nontrivial liftings of nilpotent type of quantum linear spaces and their Drinfel'd quantum doubles. We construct a family of Verma-type modules in both cases and prove a parametrization theorem for simple modules. We compute the Loewy and socle series of Verma modules under a mild restriction on the datum of a lifting. We find bases and dimensions of simple modules. |
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