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

Yucai Su, Shanghai Jiaotong University
Kaiming Zhao, Wilfrid Laurier University
Linsheng Zhu, Changshu College

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


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.