  We present a detailed analysis of the Hamiltonian constraints of the
d-dimensional tetrad-connection gravity where the non-dynamical part of the
spatial connection is fixed to zero by an adequate guage transformation. This
new action depending on the co-tetrad and the dynamical part of the spatial
connection leads to Lorentz, scalar and vectorial first-class polynomial
constraints obeying a closed algebra in terms of Poisson brackets. This algebra
closes on the structure constants instead of structure functions resulting from
the Hamiltonian formalisms based on the A.D.M. decomposition. The same algebra
of the reduced first-class constraints defined on the reduced phase-space,
where the second-class constraints are solved, is obtained in terms of Dirac
brackets. These first-class constraintslead to the same physical degrees of
freedom of the general relativity. PACS numbers: 04.20.Cv, 04.20.Fy, 11.10.Ef,
11.30.Cp
