Taking trace of vector valued differential forms Can anyone kindly give some reference on taking trace of vector valued differential forms?
Like if $A$ and$B$ are two vector valued forms then I want to understand how/why this equation is true?
$dTr(A\wedge B) = Tr(dA\wedge B) - Tr(A\wedge dB)$
One particular case in which I am interested in will be when $A$ is a Lie Algebra valued one-form on some 3-manifold. Then I would like to know what is the precise meaning/definition of $Tr(A)$ or $Tr(A\wedge dA)$ or $Tr(A\wedge A \wedge A)$? 
In how general a situation is a trace of a vector valued differential form defined? 
It would be great if someone can give a local coordinate expression for such traces. 
Any references to learn this would be of great help. 

I do not know what you mean by vector-valued form, exactly. But your equation follows from two facts:


*

*$d$ satisfies the (graded) Leinbiz equation $$d(A\wedge B) = dA\wedge B + (-1)^{\text{degree of $A$}}A\wedge dB,$$

*and $\mathrm{Tr}$ is linear and commutes with $d$, so that $$d\,\mathrm{Tr}(A)=\mathrm{Tr}\,dA.$$

