LIE ISOMORPHISMS IN *-PRIME GPI RINGS WITH INVOLUTION

Abstract

Let $R$ and $S$ be *-prime GPI rings with involution, with respective skew elements $K$ and $L$, with respective extended centroids $C$ and $D$, and let $\alpha :[K, K]/[K, K]\cap C\to [L, L]\cap D$ be a Lie isomorphism. If both involutions are of the second kind it is shown that $\alpha$ is determined by a related associative isomorphism and if the involutions are of different kinds it is shown that such a map $\alpha$ cannot exist (modulo some low-dimensional counterexamples).