Koszul duality and modular representations of semi-simple Lie algebras

Details Koszul duality and modular representations of semi-simple Lie algebras Koszul duality and modular representations of semi-simple Lie algebras

2008-03-14

arxiv.org/abs/0803.2076v3

Mathematics

Representation Theory

85 pages, final (slightly condensed) version, to appear in DMJ

Scientific paper

In this paper we prove that if G is a connected, simply-connected, semi-simple algebraic group over an algebraically closed field of sufficiently large characteristic, then all the blocks of the restricted enveloping algebra (Ug)_0 of the Lie algebra g of G can be endowed with a Koszul grading (extending results of Andersen, Jantzen and Soergel). We also give information about the Koszul dual rings. Our main tool is the localization theory in positive characteristic developed by Bezrukavnikov, Mirkovic and Rumynin.

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