For a Grothendieck category which, via a -generating sequence , is equivalent to the category of “quasi-coherent modules” over an associated -algebra , we show that under suitable cohomological conditions “taking quasi-coherent modules” defines an equivalence between linear deformations of and abelian deformations of . If is at the same time a geometric helix in the derived category, we show that restricting a (deformed) -algebra to a “thread” of objects defines a further equivalence with linear deformations of the associated matrix algebra.
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Olivier De Deken, Wendy Lowen, Abelian and derived deformations in the presence of ℤ-generating geometric helices. J. Noncommut. Geom. 5 (2011), no. 4, pp. 477–505DOI 10.4171/JNCG/83