Clifford Elements in Lie Algebras

摘要

Let L be a Lie algebra over a field F of characteristic zero or p > 3. An element c is an element of L is called Clifford if ad(c)(3) = 0 and its associated Jordan algebra L-c is the Jordan algebra F circle plus X defined by a symmetric bilinear form on a vector space X over F. In this paper we prove the following result: Let R be a centrally closed prime ring R of characteristic zero or p>3 with involution * and let c is an element of Skew(R,*) be such that c(3) = 0, c(2) not equal 0 and c(2)kc = ckc(2) for all k is an element of Skew (R, *). Then c is a Clifford element of the Lie algebra Skew(R, *).