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

This article was originally published in *Journal of Mathematical Physics, 45*(1): 525-536. © 2004 American Institute of Physics.

#### Abstract

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.

*This paper has been withdrawn.*