Algebras and Representation Theory

, Volume 16, Issue 2, pp 445–470 | Cite as

Representations of the Restricted Lie Color Algebras

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Abstract

Let \( \mathfrak{g} \) 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 \( \mathfrak{g}= {\rm{gl}} (V)\).

Keywords

Reductive Lie color algebras FP triples Baby Verma modules 

Mathematics Subject Classifications (2010)

17B50 17B10 
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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.College of SciencesChina University of Mining and TechnologyXuzhouChina

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