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

2008/04/06 by Leonid Krop, Krop, Leonid, David E. Radford +2
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA

paper · pdf · doi:10.48550/arxiv.0804.0922

arxiv created 2008/04/19 · arxiv updated 2009/12/01

Abstract

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.

Related

• Simple modules over finite quantum groups and their Drinfel'd doubles
• Factorization of simple modules for certain pointed Hopf algebras
• Quantum doubles of certain rank two pointed Hopf algebras
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