Is There a Missing Factor in the Nijenhuis Bracket Formula?

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In summary, the conversation discusses the topic of tangent-valued differential forms and the Frolicher-Nijenhuis bracket. The speaker is writing a blog post about their understanding of the subject and has noticed a missing factor in a formula mentioned in two monographs. They acknowledge that there are different conventions when dealing with differential forms, but they believe the conventions in this case are clear and yet a factor is still missing. They provide a link to their notes on the subject and the problem they are having. The conversation also briefly mentions the possibility of receiving a bucket full of snow as a means of cooling off.
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arkajad
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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...
 
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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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Related to Is There a Missing Factor in the Nijenhuis Bracket Formula?

1. What is the Nijenhuis bracket?

The Nijenhuis bracket is a mathematical operation used in differential geometry to study the curvature of manifolds. It was introduced by Dutch mathematician Albert Nijenhuis in the 1950s.

2. How is the Nijenhuis bracket calculated?

The Nijenhuis bracket is calculated using a specific formula that involves the Lie bracket, which is a mathematical operation used to study the algebraic structure of a given space.

3. What is the significance of the Nijenhuis bracket?

The Nijenhuis bracket is significant because it allows us to measure the failure of a manifold to be symplectic, which is a type of geometric structure that arises in Hamiltonian mechanics. It also plays a role in the study of integrable systems and differential equations.

4. How is the Nijenhuis bracket related to the Poisson bracket?

The Nijenhuis bracket is a generalization of the Poisson bracket, which is a mathematical operation used to study the dynamics of classical mechanical systems. The Nijenhuis bracket is more versatile and can be applied to a wider class of geometric structures.

5. Am I crazy for studying the Nijenhuis bracket?

No, you are not crazy for studying the Nijenhuis bracket. It is a complex and important mathematical concept that has applications in various fields such as physics, engineering, and computer science. Keep exploring and learning about it!

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