Abstract:

In this article, the authors obtain some results concerning derivations of finitely 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 condition for a quadratic Lie color algebra to be a double extension and further properties are given.

Key words: Derivation, central extension, double extension, quadratic Lie color algebra