Let $P\to M$ be a principal bundle over a differentiable manifold $M$, with fibre $G$, equipped with a connection $H\subset TP$. I have heard the term "infinitesimal automorphism of $H$" but I haven't been able to find the corresponding definition of a reference where this concept is explained. If I am not mistaken, the set of all infinitesimal automorphisms a connection somehow is related to a particular kind of algebroid (Courant algebroid?).
Thanks.