Loop quantum cosmology of nondiagonal Bianchi models

The nondiagonal Bianchi models are studied in the loop framework for their classical and quantum formulations. 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 a Bianchi I universe, it is shown that the geometrical operators result invariant from the diagonal description. Hence, the kinematical Hilbert space of the nondiagonal Bianchi I model has similar features to the diagonal one.