Duke Mathematical Journal
- Duke Math. J.
- Volume 154, Number 1 (2010), 31-134.
Koszul duality and modular representations of semisimple Lie algebras
In this article we prove that if is a connected, simply connected, semisimple algebraic group over an algebraically closed field of sufficiently large characteristic, then all the blocks of the restricted enveloping algebra of the Lie algebra of can be endowed with a Koszul grading (extending results of Andersen, Jantzen, and Soergel). We also give information about the Koszul dual rings. In the case of the block associated to a regular character of the Harish-Chandra center, the dual ring is related to modules over the specialized algebra with generalized trivial Frobenius character. Our main tool is the localization theory developed by Bezrukavnikov, Mirković, and Rumynin
Duke Math. J., Volume 154, Number 1 (2010), 31-134.
First available in Project Euclid: 14 July 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Riche, Simon. Koszul duality and modular representations of semisimple Lie algebras. Duke Math. J. 154 (2010), no. 1, 31--134. doi:10.1215/00127094-2010-034. https://projecteuclid.org/euclid.dmj/1279140506