ON THE CENTRALIZER OF AN AD-INVERTIBLE ELEMENT IN THE FIRST WEYL ALGEBRA OVER A NONZERO CHARACTERISTIC FIELD

In this paper, we extend the result of Guccione et al. [1] about the centralizer of an ad-invertible element to a field of nonzero characteristic. Indeed, we have proved that, in a nonzero characteristic field, for any element , if there exists such that , then the centralizer of is equal to the polynomial algebra , i.e., , where is the center of .