Selecta Mathematica

, Volume 21, Issue 2, pp 605–648 | Cite as

Koszul dual \(2\)-functors and extension algebras of simple modules for \(GL_2\)

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Abstract

Let \(p\) be a prime number. We compute the Yoneda extension algebra of \(GL_2\) over an algebraically closed field of characteristic \(p\) by developing a theory of Koszul duality for a certain class of \(2\)-functors, one of which controls the category of rational representations of \(GL_2\) over such a field.

Keywords

Koszul duality Extension algebra \(GL_2\) dg Algebra \(2\)-Functor 

Mathematics Subject Classification (2010)

16E45 (20G40) 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.School of MathematicsUniversity of East AngliaNorwichUK
  2. 2.Department of Mathematics, King’s CollegeUniversity of AberdeenAberdeenUK

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