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Quillen–Suslin theorem in a more general context

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 ...
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1 vote
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When is a Koszul algebra derived equivalent to its dual

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 ...
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4 votes
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Perfect modules for the Beilinson algebra

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/...
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