  The Hamiltonian formulation of N-bein, Einstein-Cartan, gravity, using its
first order form in any dimension higher than two, is analyzed. This
Hamiltonian formulation allows to explicitly show where peculiarities of three
dimensional case (\textit{A.M.Frolov et al, 0902.0856 [gr-qc]}) occur and make
a conjecture, based on presented in this report results, that there is one
general for \textit{all} dimensions characteristic of N-bein formulation of
gravity: after elimination of second class constraints the algebra of Poisson
brackets among remaining first class secondary constraints is the Poincare
algebra and in all dimensions N-bein, Cartan-Einstein, gravity \textit{is the
Poincare gauge theory}. The gauge symmetry corresponding to the algebra of
first class constraints has two parameters - rotational (Lorentz) and
translational. Translational invariance is common to all dimensions but some
terms in general expressions for gauge transformations of N-beins and
connections are zero in a particular, three dimensional, case.
  The proof of our conjecture is outlined in detail. Some straightforward but
tedious calculations remain to be completed to call our conjecture - a theorem
and will be reported later.

General Relativity and Quantum Cosmology;High Energy Physics - Theory