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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.

MSC:
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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