Title: Hochschild cohomology of some quantum complete intersections,
Abstract: We compute the Hochschild cohomology ring of the algebras $A= k\langle X,
Y\rangle/ (X^a, XY-qYX, Y^a)$ over a field $k$ where $a\geq 2$ and where $q\in
k$ is a primitive $a$-th root of unity. We find the the dimension of
$\mathrm{HH}^n(A)$ and show that it is independent of $a$. We compute
explicitly the ring structure of the even part of the Hochschild cohomology
modulo homogeneous nilpotent elements.