ON THE ALGEBRAIC STRUCTURE OF GRAVITY WITH TORSION INCLUDING WEYL SYMMETRY

The BRST transformations for gravity with torsion including Weyl symme try are discussed by using the so-called Maurer-Cartan horizontality c onditions. Also the coupling of scalar matter fields to gravity is inc orporated in this analysis. With the help of an operator delta which a llows to decompose the exterior space-time derivative as a BRST commut ator we solve the Wess-Zumino consistency condition corresponding to i nvariant Lagrangians and anomalies for the cases with and without Weyl symmetry.