Koszul Duality Patterns in Representation Theory

  title={Koszul Duality Patterns in Representation Theory},
  author={Alexander Beilinson and Victor Ginzburg and Wolfgang Soergel},
  journal={Journal of the American Mathematical Society},
The aim of this paper is to work out a concrete example as well as to provide the general pattern of applications of Koszul duality to repre- sentation theory. The paper consists of three parts relatively independent of each other. The first part gives a reasonably selfcontained introduction to Koszul rings and Koszul duality. Koszul rings are certain Z-graded rings with particularly nice homological properties which involve a kind of duality. Thus, to a Koszul ring one associates naturally the… 
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