On some algebras related to simple Lie triple systems

The set of nonassociative multiplications defined on any simple finite dimensional Lie triple system T over a field F of characteristic zero for which Der(T) acts as derivations is determined. It turns out that it contains nontrivial elements if and only if T is related to a simple Jordan algebra. In particular, this provides a new proof of the determination by Laquer of the invariant affine connections in the simply connected compact irreducible Riemannian symmetric spaces.


M.P. Benito <mpbenito@dmc.unirioja.es>

C. Draper <cdraper@dmc.unirioja.es>

A. Elduque <elduque@posta.unizar.es>