All Questions

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 ...

Let $KG$ be a group algebra of a finite group $G$ such that the characteristic of $K$ divides the group order. Question: When is a block of a group algebra (or even the whole group aglebra) a Koszul ...

It is well known that the principal block $\mathcal{O}_0$ of the BGG category $\mathcal{O}$ of a semisimple Lie algebra is equivalent to the category of finitely generated modules over a certain ...

Let $A$ be a finite dimensional local Frobenius algebra that is Koszul. Question: Is it true for the Koszul dual of $A$ that every finitely generated projective module is free? If not, is there a ...

Let $A$ be a finite dimensional Koszul algebra of finite global dimension. Question: When is $A$ derived equivalent to its Koszul dual algebra? I wonder whether there is an exact condition to ...

The Beilinson algebra $A=A_n$ is a finite dimensional quiver algebra that is derived equivalent to the category of coherent sheaves of $\mathcal{P}^n$. See for example https://link.springer.com/...