模李代数非限制表示中的倾斜模

Tilting modules for the nonrestricted representations of modular Lie algebra

令G为素特征p的代数闭域k上连通的简约代数群.李代数g=Lie(G),U_(χ)(g)是g的约化包络代数.在p-特征χ具有标准Levi型时,证明了一个U_(χ)(g)-模Q是倾斜模的充分必要条件是Q是投射模.

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