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

JOURNAL OF ALGEBRA

卷:420

Article

Laliena, Jesus

关键词: Associative superalgebras;    Semiprime superalgebras;    Superinvolutions;    Skewsymmetric elements;    Lie structure;   

DOI  :  10.1016/j.jalgebra.2014.07.031

来源: Elsevier

【 摘 要 】

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 boolean AND 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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free