Lie groupoids and the Frolicher-Nijenhuis bracket

Abstract

The space of vector-valued forms on any manifold is a graded Lie algebra with respect to the Frolicher-Nijenhuis bracket. In this paper we consider multiplicative vector-valued forms on Lie groupoids and show that they naturally form a graded Lie subalgebra. Along the way, we discuss various examples and different characterizations of multiplicative vector-valued forms.