Derivations of a restricted Weyl-type algebra containing the polynomial ring

A Weyl type nonassociative algebra and its subalgebra have been defined in the articles Choi and Nam (2005a,b,c); Lee and Nam (2004). Several authors have found all the derivations of some given algebra (see Ahmadi et al., 2005; Choi and Nam, 2005b; Kac, 1974; Kirkman et al., 1994; Osborn, 1997; Osborn and Passman, 1995). In this article, we find all derivations of the nonassociative algebra WP0,s1,s21 and show that the dimension of all derivations of the algebra WP0,s1,s21 is (s(1)+s(2))(2)+s(1)+s(2). Because of the dimension of a derivation algebra, we know that if s(1)+s(2)s(1)'+s(2)', then the algebras WP0,s1,s21 and WP0,s1',(s21)' are not isomorphic.