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Why we are interested to find whether an algebra is Koszul or not? What is the significance of being Koszul? Only this that we will know certain homological invariants of the algebra like projective dimension, Betti numbers, regularity etc or some other things also?

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    $\begingroup$ There is a discussion you might find interesting in the introduction of "Quadratic Algebras" by Polishchuk and Positselski. $\endgroup$ – Captain Lama Jun 3 at 20:48
  • $\begingroup$ yes.thank you very much. $\endgroup$ – user118827 Jun 4 at 6:19
  • $\begingroup$ but I still need a more satisfying answer. $\endgroup$ – user118827 Jun 4 at 6:21

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