Classification of Derivation-Simple Color Algebras Related to Locally Finite Derivations

We classify the pairs (A, D) consisting of an (∈, Γ)-color-commutative associative algebra A with an identity element over an algebraically closed field F of characteristic zero and a finite dimensional subspace D of (∈, Γ)-color-commutative locally finite color-derivations of A such that A is Γ-graded D-simple and the eigenspaces for elements of D are Γ-graded. Such pairs are the important ingredients in constructing some simple Lie color algebras which are in general not finitely-graded. As some applications, using such pairs, we construct new explicit simple Lie color algebras of generalized Witt type, Weyl type