Questions tagged [koszul-duality]

Question: Consider quadratic algebra with four generators $a,b,c,d,d$ and three relations $ac=ca,bd = db, ad-da = cb - bc$ . Is it a Koszul algebra ? (i.e. Koszul complex is resolution of ground field ...

Okay, let's make sure I'm on the same page with those who know homological algebra. What is Koszul duality in general? What does it mean that categories are Koszul dual (I guess representations of ...

Koszul duality Given a finite-dimensional $k$-vector space $V$ (I am happy taking $k = \mathbb{C}$ anywhere in the following if it makes a difference) and a subspace $R \subseteq V \otimes V$, we can ...

Let $A$ and $B$ be $A_\infty$-algebras. It's true, but it's a quite nontrivial fact, that the tensor product $A \otimes B$ can be given the structure of $A_\infty$-algebra, too. What is much easier to ...

If $G$ is an algebraic group, then one can show $\operatorname{H}^*(BG,k)$ and $\operatorname{H}_*(G,k)$ are Koszul dual dg algebras, e.g. Drinfeld and Gaitsgory, "Finiteness questions for ...

$\newcommand{\dual}{\mathrm{dual}}\DeclareMathOperator\End{End}\DeclareMathOperator\Fun{Fun}\DeclareMathOperator\Spec{Spec}\DeclareMathOperator\GL{GL}$Around 1986–7 Yu.Manin proposed natural and ...