Lagrangian generators of the Poincaré gauge symmetries

We have systematically computed the generators of the symmetries arising in Poincaré gauge theory formulation of gravity, both in $2+1$ and $3+1$ dimensions. This was done using a completely Lagrangian approach. The results are expected to be valid in any dimensions, as seen through lifting the results of the $2+1$ dimensional example into the $3+1$ dimensional one.

Figure 1

The scheme for Lagrangian analysis of Poincaré gauge theory: symmetries, corresponding gauge identities, and generators in $2+1$ and $3+1$ dimensions.