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Results tagged with koszul-duality
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user 1306
Questions relating to various versions of Koszul duality, including Koszul duality between algebras and Koszul duality for operads.
11
votes
Accepted
Koszulness of the cohomology ring of moduli of stable genus zero curves
It is: https://arxiv.org/abs/1902.06318 - this paper also explains how to use the Koszul dual algebra for something, where something is estimating Betti numbers of the free loop spaces of $\overline{M …
- 16.9k
7
votes
Accepted
Does Manin's construction of non-commutative endomorphism algebra $\mathrm{End}(A)$ produce ...
Q1: This algebra is just the Manin black product of $A$ and $A^!$ (in other words, the Koszul dual of the Segre product of $A$ and $A^!$), and hence it is Koszul. (As requested, the Segre product of t …
- 16.9k
5
votes
Accepted
Infinity-homotopies
I don't know if you found an answer since you posted the question, but I will write this just in case: there is a "cute" (easy) definition in case of nonsymmetric operads which generalises the A-infin …
- 16.9k
3
votes
Accepted
Differential of the Twisted complex for algebraic operads
Since $\alpha$ is of degree $-1$, these terms come in pairs appearing with opposite signs that cancel each other. In other words, the (co)associativity for (co)operads has a sequential axiom and a par …
- 16.9k