On the Algebraic Structure of Gravity with Torsion including Weyl symmetry

The BRST transformations for gravity with torsion including Weyl symmetry are discussed by using the so-called Maurer-Cartan horizontality conditions. Also the coupling of scalar matter fields to gravity is incorporated in this analysis. With the help of an operator $\d$ which allows to decompose the exterior space-time derivative as a BRST commutator we solve the Wess-Zumino consistency condition corresponding to invariant Lagrangians and anomalies for the cases with and without Weyl symmetry.