Lie structure in semiprime superalgebras with superinvolution

In this paper we investigate the Lie structure of the Lie superalgebra K of skew elements of a semiprime associative superalgebra A with superinvolution. We show that if U is a Lie ideal of K, then either there exists an ideal J of A such that the Lie ideal [J∩K,K] is nonzero and contained in U, or A is a subdirect sum of A′, A″, where the image of U in A′ is central, and A″ is a subdirect product of orders in simple superalgebras, each at most 16-dimensional over its center.