Operators on Differential Forms for Transformation Groups

For any Lie group action S: GP P , we introduce C (P )linear operators S i , that transform n-forms n A n (P, V ) into (n-i)-forms S i n A n-i (P, Alt i (g, V )).We compute the exterior derivative of these generated forms and their behavior under interior products with vector fields and Lie differentiation.By combination with Lie algebra valued forms A 1 (P, g) and p A p (P, g), we recover V -valued forms S A n (P, V ), resp., ( s n S ) p for s n A n (P, Hom( s g, V )) and compute their exterior derivative.The derived formulae play an important role for local evaluations of connections on fiber bundles.Math.