TITLE: Reference for Lie-algebra valued differential forms
QUESTION [15 upvotes]: I am learning about vector-valued differential forms, including forms taking values in a Lie algebra. On Wikipedia there is some explanation about these Lie algebra-valued forms, including the definition of the operation $[-\wedge -]$ and the claim that "with this operation the set of all Lie algebra-valued forms on a manifold M becomes a graded Lie superalgebra".
The explanation on Wikipedia is a little short, so I'm looking for more information about Lie algebra-valued forms. Unfortunately, the Wikipedia page does not cite any sources, and a Google search does not give very helpful results.

Where can I learn about Lie algebra valued differential forms?

In particular, I'm looking for a proof that $[-\wedge -]$ turns the set of Lie algebra-valued forms into a graded Lie superalgebra. I would also appreciate some information about how the exterior derivative $d$ and the operation $[-\wedge -]$ interact.

REPLY [5 votes]: I studied it from Differential Geometry Connections,Curvature and Characteristic Classes by Loring W.Tu in the Chapter 4, Section 21(specially subsection 21.5). The whole section 21 (Vector-valued forms) is very well treated. As a Special case Lie-Algebra valued differential forms are discussed. Also how a vector valued differential form differ from a real valued form is discussed in 21.10. Say for example on the Lie Algebra of $Gl(n,\mathbb{R})$, 
 $\alpha\wedge\alpha$ which is given by Matrix Multiplication is not always zero when the deree of $\alpha $ is odd which is contradictory to the usual notion of Real Valued differential form.