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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.
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
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
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
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