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15 July 2010 Koszul duality and modular representations of semisimple Lie algebras
Simon Riche
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Duke Math. J. 154(1): 31-134 (15 July 2010). DOI: 10.1215/00127094-2010-034

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

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Simon Riche. "Koszul duality and modular representations of semisimple Lie algebras." Duke Math. J. 154 (1) 31 - 134, 15 July 2010. https://doi.org/10.1215/00127094-2010-034

Information

Published: 15 July 2010
First available in Project Euclid: 14 July 2010

zbMATH: 1264.17005
MathSciNet: MR2668554
Digital Object Identifier: 10.1215/00127094-2010-034

Subjects:
Primary: 17B20
Secondary: 16E45, 16S37

Rights: Copyright © 2010 Duke University Press

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Vol.154 • No. 1 • 15 July 2010
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