Representations of the Restricted Lie Color Algebras

Let be a restricted Lie color algebra. We define the p -character χ and study the χ -reduced enveloping algebras. We define the reductive Lie color algebras and FP triples, and study the representations associated with FP triples. As an application, we prove an analogue of the Kac-Weisfeiler theorem and determine the simplicity of the baby Verma module for the general linear Lie color algebra .