Derivations and extensions of lie color algebra

In this article, the authors obtain some results concerning derivations of fi-nitely generated Lie color algebras and discuss the relation between skew derivation space SkDer(L) and central extension H2(L, F) on some Lie color algebras. Meanwhile, they generalize the notion of double extension to quadratic Lie color algebras, a sufficient con-dition for a quadratic Lie color algebra to be a double extension and further properties are given.