Factorization of simple modules for certain restricted two-parameter quantum groups

Abstract

We study the representations of the restricted two-parameter quantum groups of types B and G. For these restricted two-parameter quantum groups, we give some explicit conditions which guarantee that 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. That is, given θ a primitive lth root of unity, the factorization of simple {}_{{\theta }^y,{\theta }^z},\left(\right)-\mathrm{modules} is possible, if and only if (2(y - z), l) = 1 for ={}_{2n+1}; (3(y - z), l) = 1 for g= G₂.

Key words： Hopf algebra; Drinfel’d double; restricted two-parameter quantum group

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