  We give a description of the Hochschild cohomology for noncommutative planes
(resp. quadrics) using the automorphism groups of the elliptic triples (resp.
quadruples) that classify the Artin-Schelter regular $\mathbb{Z}$-algebras used
to define noncommutative planes and quadrics. For elliptic triples the
description of the automorphism groups is due to Bondal-Polishchuk, for
elliptic quadruples it is new.
