On Certain Semiprime Associative Superalgebras

Abstract

In this note we emphasise the relationship between the structure of an associative superalgebra with superinvolution and the structure of the Lie substructure of skewsymmetric elements. More explicitly, we show that if A is a semiprime associative superalgebra with superinvolution and K is the Lie superalgebra of skewsymmetric elements satisfying [K 2, K 2] = 0, then A is a subdirect product of orders in simple superalgebras each at most 4-dimensional over its center.