Modules over restricted supersolvable Lie algebras (Q1885193)

Let \(F\) be an algebraically closed field of characteristic \(p\) and \(L\) be a finite-dimensional supersolvable restricted Lie algebra over \(F\). Let \(C(L)\) be the center of \(L\) and \(T_p(L)\) be the maximal toral ideal contained in \(C(L)\). The author proves that if \(C(L)\neq T_p(L)\), then a simple module over \(L\) is not projective. The author also studies when a module contains projective summands of an arbitrary finite-dimensional module over a unimodular Lie algebra.