Abstract :
LetKbe a field and let : Γ × Γ → K•be a bicharacter defined on the multiplicative group Γ. We suppose thatAis a Γ-graded, associativeK-algebra that is color commutative with respect to . Furthermore, let Δ be a nonzero Γ-graded,K-vector space of color derivations ofAand suppose that Δ is also color commutative with respect to the bicharacter . Then, with a rather natural definition,A K Δ = AΔ becomes a Lie color algebra, and we obtain necessary and sufficient conditions here for this Lie color algebra to be simple. With two minor exceptions when dimK Δ = 1, simplicity occurs if and only ifAis graded Δ-simple andAΔ Δ = AΔΔ acts faithfully as color derivations onA.
