A technique for analyzing the structure of isometries

A new technique is introduced to investigate the structure of isometry Lie algebras. Some general results are first proved by applying this technique to n-dimensional manifolds equipped with metrics of arbitrary signature. A restriction is then made to 3-manifolds representing the space of orbits of the timelike Killing field in stationary space-times. Under the assumption of asymptotic flatness at spatial infinity, a complete description of isometry Lie algebras of these 3-manifolds is obtained. As corollaries, several results about symmetries of stationary isolated systems in general relativity are proved.