The computation of the Conformal Killing Vectors of an 1+(n-1) decomposable metric

A generalisation of a known theorem concerning the computation of the conformal algebra in 1+(n-1) decomposable spaces is presented. It is shown that the general form of Conformal Vector Fields (CVF) is the sum of a gradient CVF and a Killing or Homothetic (n-1)-vector. A simple criterion is established which enables one to check if a 1+(n-1) decomposable spacetime admits proper CVF. As an example, the complete conformal algebra of a G\"odel-type spacetime is computed.