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Hochschild cohomology of noncommutative planes and quadrics

Banff International Research Station for Mathematical Innovation and Discovery

The Hochschild cohomology of an abelian category describes the infinitesimal deformation theory of this abelian category in the sense of Lowen--Van den Bergh. Applying this to the category coh X for a variety X gives information on how the noncommutative deformations of this variety behave. In this talk I will explain how to compute the Hochschild cohomology of the abelian category qgr A for a quadratic (resp. cubic) 3-dimensional Artin--Schelter regular algebra, i.e. for a noncommutative projective plane (resp. noncommutative quadric surface). The main ingredients for this are the full and strong exceptional collection in the derived category and the classification of these algebras using the geometry of the point scheme.

Mathematics; Associative rings and algebras; Algebraic geometry; Algebraic structures

video/mp4

Author affiliation: University of Antwerp

2017-03-14

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60878

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/