Factorization of simple modules for certain pointed Hopf algebras |
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Authors: | Mariana Pereira |
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Affiliation: | aCentro de Matemática, Facultad de Ciencias, Iguá 4225, Montevideo 11400, Uruguay |
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Abstract: | We study the representations of two types of pointed Hopf algebras: restricted two-parameter quantum groups, and the Drinfel'd doubles of rank one pointed Hopf algebras of nilpotent type. We study, in particular, under what conditions a simple module can be factored as the tensor product of a one-dimensional module with a module that is naturally a module for the quotient by central group-like elements. For restricted two-parameter quantum groups, given θ a primitive ℓth root of unity, the factorization of simple -modules is possible, if and only if gcd((y−z)n,ℓ)=1. For rank one pointed Hopf algebras, given the data , the factorization of simple -modules is possible if and only if |χ(a)| is odd and |χ(a)|=|a|=|χ|. Under this condition, the tensor product of two simple -modules is completely reducible, if and only if the sum of their dimensions is less than or equal to |χ(a)|+1. |
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Keywords: | Hopf algebras Drinfel'd double Quantum groups |
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