  Motivated by the classical Noether's problem, J. Alev and F. Dumas proposed
the following question, commonly referred to as the noncommutative Noether's
problem: Let a finite group $G$ act linearly on $\mathbb{C}^n,$ inducing the
action on $\text{Frac}(A_n(\mathbb{C}))$-the skew field of fractions of the
$n$-th Weyl algebra $A_n(\mathbb{C}),$ then is $\text{Frac}(A_n(\mathbb{C}))^G$
isomorphic to $\text{Frac}(A_n(\mathbb{C}))?$ In this note we show that if
$\text{Frac}(A_n(\mathbb{C})^{G}\cong \text{Frac}(A_n(\mathbb{C})),$ then for
any algebraically closed field $k$ of large enough characteristic, field
$k(x_1,\cdots, x_n)^G$ is stably rational. This result allows us to produce
counterexamples to the noncommutative Noether's problem based on well-known
counterexamples to the Noether's problem for algebraically closed fields.
