On the Lie Structure of the Skew Elements of a Simple Superalgebra with Superinvolution

We investigate the Lie structure of the Lie superalgebraKof skew elements of a unital simple associative superalgebraAwith superinvolution over a field of characteristic not 2. It is proved that ifAis more than 16-dimensional over its centerZ, then any Lie idealUofKsatisfies eitherU ZorU [K, K]; moreover, any Lie idealUof [K, K] satisfies eitherU ZorU = [K, K]. In particular, [K, K]/(Z ∩ [K, K]) is a simple Lie superalgebra.