Simple Lie color algebras of Witt type

Let EI be a field and let epsilon: Gamma x Gamma --> K . be a bicharacter defined on the multiplicative group Gamma. We suppose that A is a Gamma-gradsd, associative K-algebra that is color commutative with respect to epsilon. Furthermore, let Delta be a nonzero Gamma-graded, K-vector spare of color derivations of A and suppose that Delta is also color commutative with respect to the bicharacter epsilon. Then, with a rather natural definition, A x(K) Delta = A Delta 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 dim, Delta = 1, simplicity occurs if and only if A is graded h-simple and A(Delta) x Delta = A(Delta)Delta acts faithfully as color derivations on A. (C) 1998 Academic.