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Is it known the maximal class of Koszul algebras for which any deformation is Koszul?

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It would be very helpful if you provide some motivation, say what you already know, and what class of deformations you are interested in, as well as what definition of Koszulness you work with (e.g. are your algebras homogeneous, connected, over a field etc.). Without that, this question is a bit too vague and lazy. – Vladimir Dotsenko Feb 20 '13 at 17:50

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