Kohomologie von p-Lie-Algebren und nilpotente Elemente. (Cohomology of p- Lie-algebras and nilpotent elements)
Let \({\mathfrak g}\) be a finite dimensional p-Lie algebra over an algebraically closed field k of characteristic \(p>0\). If M is a restricted module for \({\mathfrak g}\), then \(H_*({\mathfrak g},M)\) denotes the restricted cohomology of M. Then the variety attached to M is the variety \(V_{{\mathfrak g}}(M)\) defined by the annihilator in S(\({\mathfrak g}^*)\) of H(\({\mathfrak g},M\otimes M^*)\). It is first proved that \(V_{{\mathfrak g}}(k)\) consists of those elements in \({\mathfrak g}\) which are killed by the p-th power map and next that if either \(p=2\) or if \({\mathfrak g}\) is unipotent, then \(V_{{\mathfrak g}}(M)=\{x\in V_{{\mathfrak g}}(k)|\) M's restriction to kx is not injective\(\}\cup \{0\}\). The last statement was soon after proved for all \({\mathfrak g}\) by \textit{E. M. Friedlander} and \textit{B. J. Parshall} [Invent. Math. 86, 553-562 (1986)].
scientific article; zbMATH DE number 3993812
scientific article