Hochschild cohomology of some quantum complete intersections

We compute the Hochschild cohomology ring of the algebras $A= k\langle X, Y\rangle/ (X^a, XY-qYX, Y^a)$overafield$k$where$a\geq 2$andwhere$q\in k$isaprimitive$a$-throotofunity\mathrm{.}Wefindthethedimensionof$$\mathrm{H}\mathrm{H}$^n(A)$andshowthatitisindependentof$a$. We compute explicitly the ring structure of the even part of the Hochschild cohomology modulo homogeneous nilpotent elements.