Is There a Missing Factor in the Nijenhuis Bracket Formula?

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So, I am learning about tangent-valued differential forms, operations on forms and Frolicher-Nijenhuis bracket, and I am writing a blog about what I have learned. In two monographs I have spotted a formula that - as far as can see - has a missing factor.

At least this is how I understand what is written. Of course when we deal with differential forms, there are at least two different conventions and this needs to be taken into account. But I think in this case the conventions are clear and yet a factor seems to be missing.

My notes on the subject and the problem I am having is http://arkadiusz-jadczyk.eu/blog/?p=324".

A bucket full of cold water on my head will be greatly appreciated.
 
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If your'e living in Europe I'll give you a bucket full of snow...
 
MathematicalPhysicist said:
If your'e living in Europe I'll give you a bucket full of snow...

I believe snow is also available in the US http://www.reuters.com/article/idUSN2722234420101227"
 
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