Automorphism groups of Weyl-type algebras

Let F be a field of characteristic 0, x(1), x(2),..., x(n) be n commuting variables over F, and F(x(1), x(2),..., x(n)) be the field of all rational functions. Let D = +(n)(i=1) Fx(i) partial derivative/partial derivativex(i). We have the simple Weyl type algebra A = F(x(1), x(2),..., x(n))[D]. In this paper, the automorphism group Aut A of the associative algebra A and the automorphism group AutA(L) of the Lie algebra A(L) are determined, and it is proved that Aut A(L) = Z(2) x Aut A.