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The necessary and sufficient conditions for a spacetime with an invariantframe to admit a group of isometries of dimension $r$ are given in terms of theconnection tensor $H$ associated with this frame. In Petrov-Bel types I, II andIII, and in other spacetimes where an invariant frame algebraically defined bythe curvature tensor exists, the connection tensor $H$ is given in terms of theWeyl and Ricci tensors without an explicit determination of the frame. Thus, anIDEAL (intrinsic, deductive, explicit and algorithmic) characterization ofthese spacetimes follows. Some examples show that this algorithm can be easilyimplemented on the xAct Mathematica suite of packages.

Dimension of the isometry group in spacetimes with an invariant frame