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 $\text{char}\,k > 0$?



Center of $k$-algebra with two generators and sole defining relation $yx - xy = 1$ when $\text{char}\,k > 0$
This is the [Weyl algebra](https://en.wikipedia.org/wiki/Weyl_algebra). The center is $k[x^p,y^p]$, where $p$ is the characteristic. See, for example, [here](https://math.stackexchange.com/questions/129834/) for a proof.


