Representations of pointed Hopf algebras and their Drinfel'd quantum doubles

Details Representations of pointed Hopf algebras and their Drinfel'd quantum doubles Representations of pointed Hopf algebras and their Drinfel'd quantum doubles

2008-04-06

arxiv.org/abs/0804.0922v2

Mathematics

Quantum Algebra

Scientific paper

We study representations of nilpotent type nontrivial liftings 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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