  We extend the analysis of the Hamiltonian formalism of the d-dimensional
tetrad-connection gravity to the fermionic field by fixing the non-dynamic part
of the spatial connection to zero. Although the reduced phase space is equipped
with complicated Dirac brackets, the first-class constraints which generate the
diffeomorphisms and the Lorentz transformations satisfy a closed algebra with
structural constants analogous to that of the pure gravity. We also show the
existence of a canonical transformation leading to a new reduced phase space
equipped with Dirac brackets having a canonical form leading to the same
algebra of the first-class constraints.
