Generalized Derivations Of Lie Color Algebras

In this thesis, we mainly study the derivation algebras Der(L), the center deriva-tion algebras ZDer(L), the quasiderivation algebras QDer(L). and the generalized derivation algebras GDer(L) of Lie color algebra L, which form a tower ZDer(L)(?) Der(L)(?)QDer(L)(?)GDer(L)(?)P1(L). We give some basic properties of the gen-eralized derivation algebras and their Lie subalgebras. show that the quasicentroid of a Lie color algebra is also a Lie color algebra if and only if it is an associative color algebra and prove that the quasiderivations of L can be embedded as derivations in a larger Lie color algebra L. Moreover, when the center of L is equal to zero, we obtain a direct sum decomposition of Der(L).