Journal of Noncommutative Geometry

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Volume 13, Issue 2, 2019, pp. 769–795
DOI: 10.4171/JNCG/338

Published online: 2019-07-25

Hochschild cohomology of noncommutative planes and quadrics

Pieter Belmans[1]

(1) Universität Bonn, Germany

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 these automorphism groups is due to Bondal–Polishchuk, for elliptic quadruples it is new.

Keywords: Noncommutative algebraic geometry, noncommutative planes, Hochschild cohomology

Belmans Pieter: Hochschild cohomology of noncommutative planes and quadrics. J. Noncommut. Geom. 13 (2019), 769-795. doi: 10.4171/JNCG/338