  Beside diffeomorphism invariance also manifest SO(3,1) local Lorentz
invariance is implemented in a formulation of Einstein Gravity (with or without
cosmological term) in terms of initially completely independent vielbein and
spin connection variables and auxiliary two-form fields. In the systematic
study of all possible embeddings of Einstein gravity into that formulation with
auxiliary fields, the introduction of a ``bi-complex'' algebra possesses
crucial technical advantages. Certain components of the new two-form fields
directly provide canonical momenta for spatial components of all Cartan
variables, whereas the remaining ones act as Lagrange multipliers for a large
number of constraints, some of which have been proposed already in different,
less radical approaches. The time-like components of the Cartan variables play
that role for the Lorentz constraints and others associated to the vierbein
fields. Although also some ternary ones appear, we show that relations exist
between these constraints, and how the Lagrange multipliers are to be
determined to take care of second class ones. We believe that our formulation
of standard Einstein gravity as a gauge theory with consistent local Poincare
algebra is superior to earlier similar attempts.
