The kinematical role of automorphisms in the orthonormal frame approach toBianchi cosmology

The automorphism group and frame commutator relations in the orthonormal fr ame approach to Bianchi cosmology are used to construct an explicit coordin ate representation of the orthonormal frame itself (and hence of the spacet ime metric) which depends algebraically on the connection coefficients. Thi s is not possible in general inhomogeneous models where differential equati ons must instead be solved. The shift vector field required for this proced ure is intimately related to the true Smarr-York minimal strain and minimal distortion shifts. (C) 1999 American Institute of Physics. [S0022-2488(99) 01701-6].