Quadratic Lie superalgebras with the completely reducible action of the even part of the odd part (Q1969130)

A quadratic Lie superalgebra is a Lie superalgebra \({\mathfrak g} = {\mathfrak g}_{\overline 0} + {\mathfrak g}_{\overline 1}\) with a nondegenerate, supersymmetric, consistent, \(\mathfrak g\)-invariant bilinear form. The author classifies all such algebras that are finite-dimensional over an algebraically closed field of characteristic zero and for which \({\mathfrak g}_{\overline 0}\) is a reductive Lie algebra and the action of \({\mathfrak g}_{\overline 0}\) on \({\mathfrak g}_{\overline 1}\) is completely reducible. Some results are also obtained in the case that \({\mathfrak g}_{\overline 0}\) is not assumed to be reductive.