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Koszul duality and modular representations of semisimple Lie algebras. (English) Zbl 1264.17005
In this paper the author proves Koszulity for all blocks of the restricted enveloping algebra of a connected, simply connected, semisimple algebraic group over an algebraically closed field of sufficiently large characteristic. In many cases the author also presents a description for the Koszul dual. Proofs use geometric descriptions of the derived module categories and explicit information about geometric counterparts of translation functors and their Koszul duals.

17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
17B35 Universal enveloping (super)algebras
20G05 Representation theory for linear algebraic groups
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