DERIVATIONS OF A COMBINATORIAL LIE ALGEBRA

Abstract

We consider the simple antisymmetrized algebra <TEX>$N(e^{A_P},n,t)_1^-$</TEX>. The simple non-associative algebra and its simple subalgebras are defined in the papers [1], [3], [4], [5], [6], [8], [13]. Some authors found all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra in their papers [2], [3], [5], [7], [9], [10], [13], [15], [16]. We find all the derivations of the Lie subalgebra <TEX>$N(e^{{\pm}x_1x_2x_3},0,3)_{[1]}{^-}$</TEX> of <TEX>$N(e^{A_p},n,t)_k{^-}$</TEX> in this paper.