Automorphism groups of Weyl-type algebras. (Q1598152)

For \(F\) a field of characteristic zero, \(x_1,x_2,\dots,x_n\) commuting variables over \(F\), \(F(x_1,x_2,\dots,x_n)\) the field of all rational functions, and \(D=\bigoplus_{i=1}^nFx_i \tfrac\partial{\partial x_i}\), the associative algebra \(\mathcal A\) is defined as \(F(x_1,x_2,\dots,x_n)[D]\) with product the composition of operators on \(F(x_1,x_2,\dots,x_n)\). The authors determine the automorphism group \(\Aut{\mathcal A}\) of the algebra \(\mathcal A\) and show that the automorphism group \(\Aut{\mathcal A}_L\) of the induced Lie algebra of \(\mathcal A\) is equal to \(\mathbb{Z}_2\ltimes\Aut{\mathcal A}\).