Lie structure in semiprime superalgebrs 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 a determined nonzero Lie ideal connected with J is 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.