简约模李代数的上同调(英文)

Cohomology of reductive modular Lie algebras

令G为素特征代数闭域上简约连通的代数群,g是G的李代数.本文研究当p-特征χ具有标准Levi型时简约模李代数g的上同调.当baby Verma模的最高权为p-正则时,得到了baby Verma模和扭baby Verma模之间的扩张群非分裂的充分必要条件.

Let G be a connected reductive algebraic group over an algebraically closed field k of prime characteristic p, and g = Lie（G）. This paper studied the cohomology of the reductive Lie algebra g with p-character X of standard Levi form. When the highest weight of baby Verma module is p-regular, the necessary and sufficient condition for the Ext groups between baby Verma module and twist baby Verma module being non-split was gotten.