The cohomology of modular Lie algebras with coefficients in a restricted Verma module (Q1801720)

Let \(\mathfrak g\) be a classical semisimple Lie algebra over an algebraically closed field \(F\), \(\text{char }F=p>0\), and \(Z(\lambda)\) denote the restricted Verma module of \(\mathfrak g\). The author determines the structure of the cohomology of \(\mathfrak g\) with coefficients in \(Z(\lambda)\). By Shapiro's lemma and the Hochschild-Serre spectral sequence, the computation of \(H^*({\mathfrak g},Z(\lambda))\) can be reduced to the computation of the cohomology of a nilradical \(\mathfrak n\) in certain modules. The latter can be computed by Kostant's fundamental results generalized to the modular case.