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 -algebras used to define noncommutative planes and quadrics. For elliptic triples the description of these automorphism groups is due to Bondal–Polishchuk, for elliptic quadruples it is new.
Cite this article
Pieter Belmans, Hochschild cohomology of noncommutative planes and quadrics. J. Noncommut. Geom. 13 (2019), no. 2, pp. 769–795DOI 10.4171/JNCG/338