  The non-diagonal Bianchi models are studied in the loop framework for their
classical and quantum formulation. The expressions of the
Ashtekar-Barbero-Immirzi variables and their properties are found to provide a
loop quantization of these models. In the special case of Bianchi I Universe,
it is shown that the geometrical operators result invariant from the diagonal
description. Hence, the kinematical Hilbert space of the non-diagonal Bianchi I
model has similar features to the diagonal one.

General Relativity and Quantum Cosmology