Hochschild cohomology of noncommutative planes and quadrics

Abstract

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.

27 pages, accepted for publication in Journal of Noncommutative Geometry

Cited by in corpus (6)

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• Admissible subcategories in derived categories of moduli of vector bundles on curves
• Polyvector fields for Fano 3-folds
• Automorphisms of Hilbert schemes of points on surfaces
• Hochschild cohomology related to graded down-up algebras with weights $(1,n)$
• Hochschild cohomology of Beilinson algebras of graded down-up algebras with weights ($n,m$)