Center of $k$-algebra with two generators and sole defining relation $yx - xy = 1$ when $\text{char}\,k > 0$

Question

Let $A(k)$ be a $k$-algebra with two generators, $x$, $y$, and one defining relation: $yx - xy = 1$. What is the center of the algebra $A(k)$ in the case $\text{char}\,k > 0$?

Answer 1

This is the Weyl algebra. The center is $k[x^p,y^p]$, where $p$ is the characteristic. See, for example, here for a proof.