Symmetric Self-dual Lie Color Algebras

In this paper,we make use of cohomological way to study finite dimensional symmetric self-dual Lie color algebras.The main results are the following:(1)We generalize the notion of double extension to finite dimensional symmetric self-dual Lie color algebras and obtain some important results;(2)We give a sufficient condition for a finite dimensional symmetric self-dual Lie color algebras to be a double extension,thus we solve its classification in the sense of cohomology;(3)We generalize the notion of T~*-extension to symmetric self-dual Lie color algebras and give a necessary and sufficient condition for a finite dimensional symmetric self-dual Lie color algebras to be a T~*-extension.