Representations for the restricted Lie color algebras

TL;DR

This paper develops the theory of representations for restricted Lie color algebras, establishing analogues of classical theorems and characterizing module simplicity in this generalized setting.

Contribution

It introduces generalized p-characters for restricted Lie color algebras and determines simplicity criteria for modules, extending classical results to this broader context.

Findings

Defined generalized p-characters for restricted Lie color algebras

Established an analogue of the Kac-Weisfiler theorem for algebraic Lie color algebras

Determined the simplicity conditions for baby Verma modules

Abstract

The generalized p-characters for the restricted Lie color are defined. The simplicity of the induced modules for the FP triples are determined. As applications, we have obtained an analogue of the Kac-Weisfiler theorem for the algebraic Lie color algebra cgl(V), also determined the simplicity of the baby Verma modules for cgl(V).