DERIVATIONS OF A WEYL TYPE NON-ASSOCIATIVE ALGEBRA ON A LAURENT EXTENSTION

Abstract

A Weyl type algebra is defined in the book ([4]). A Weyl type non-associative algebra <TEX>$\={WP_{m,n,s}}$</TEX> and its restricted sub-algebra <TEX>$\={WP_{m,n,s_{\gamma}}}$</TEX> are defined in various papers ([1], [12], [3], [11]). Several authors 0nd all the derivations of an associative (Lie or non-associative) algebra in the papers ([1], [2], [12], [4], [6], [11]). We find all the non-associative algebra derivations of the non-associative algebra <TEX>$\={WP_{0,2,0_B}$</TEX>, where <TEX>$B=\{{\partial}_0,\;{\partial}_1,\;{\partial}_2,\;{\partial}_{12},\;{\partial}^2_1,\;{\partial}^2_2\}$</TEX>.