Lie Quotients for Skew Lie Algebras.

Let A be a semiprime associative algebra with an involution ∗ over a field of characteristic not 2, let KA be the Lie algebra of all skew elements of A, and let ZKA denote the annihilator of KA. The aim of this paper is to prove that if Q is a ∗-subalgebra of Qs(A) (the Martindale symmetric algebra of quotients of A) containing A, then KQ/ZKQ is a Lie algebra of quotients of KA/ZKA. Similarly, [KQ, KQ]/Z[KQ,KQ] is a Lie algebra of quotients of [KA,KA]/Z[KA,KA]. [ABSTRACT FROM AUTHOR]