What is the intuition behind Koszul graded-commutative algebras and Lie algebras? Why is it an interesting property to study in commutative algebra? I know why it's interesting in homotopy theory but what about in algebraic geometry or commutative algebra?
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Your terminology is a little ambiguous; there is something called a Koszul algebra (https://en.wikipedia.org/wiki/Koszul_algebra) but your use of "Koszul commutative" makes it sound like you might be referring to graded-commutative algebras and Lie algebras? – Qiaochu Yuan Oct 17 '23 at 21:25
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I'm asking about graded or ungraded commutative algebras and Lie algebras which are Koszul. – joe Oct 18 '23 at 22:32
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We can view ungraded things (vector space, modules, algebras) as graded things concentrated in degree zero. Could you please be more specific on what is ambiguous? – joe Oct 18 '23 at 22:41