Duke Mathematical Journal

Koszul duality and modular representations of semisimple Lie algebras

Simon Riche

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In this article we prove that if G 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 (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. In the case of the block associated to a regular character λ of the Harish-Chandra center, the dual ring is related to modules over the specialized algebra (Ug)λ with generalized trivial Frobenius character. Our main tool is the localization theory developed by Bezrukavnikov, Mirković, and Rumynin

Article information

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

Primary: 17B20: Simple, semisimple, reductive (super)algebras
Secondary: 16S37: Quadratic and Koszul algebras 16E45: Differential graded algebras and applications


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

Export citation