Abstract:

Let $ G $ be a connected reductive algebraic group over an algebraically closed field $ k $ of prime characteristic $ p $ , and let $ {\frak {g}} = {\rm{Lie}}(G) $ , $U_{\chi}({\frak {g}}) $ be the reduced enveloping algebra. In this paper, when $ p $ -character $ \chi $ has the standard Levi form, we prove that a $ U_{\chi}({\frak {g}}) $ -module $ Q $ is a tilting module if and only if it is projective.

Key words: tilting module, standard Levi form, projective module, nonrestricted representation