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arXiv · 1307.3163

The derived superalgebra of skew elements of a semiprime superalgebra with superinvolution

Jesus Laliena
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Abstract

In this paper we investigate the Lie structure of the derived Lie superalgebra [K, K], with K the set of skew elements of a semiprime associative superalgebra A with superinvolution. We show that if U is a Lie ideal of [K, K], then either there exists an ideal J of A such that the Lie ideal [J \cap 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.

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Jesus Laliena. 2013-07-11. The derived superalgebra of skew elements of a semiprime superalgebra with superinvolution. https://arxiv.org/abs/1307.3163

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