Duke Mathematical Journal

Koszul duality and modular representations of semisimple Lie algebras

Simon Riche

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Abstract

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

Source
Duke Math. J., Volume 154, Number 1 (2010), 31-134.

Dates
First available in Project Euclid: 14 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1279140506

Digital Object Identifier
doi:10.1215/00127094-2010-034

Mathematical Reviews number (MathSciNet)
MR2668554

Zentralblatt MATH identifier
1264.17005

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

Citation

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


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