Schouten identity resembles Jacobi identity

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SUMMARY

The discussion centers on the resemblance between the Schouten identity and the Jacobi identity, highlighting their structural similarities. The Schouten identity, represented as

+

+

= 0, features a dummy variable 'p' in each term, facilitating a correspondence with the Jacobi identity, expressed as [A,[B,C]] + [C,[A,B]] + [B,[C,A]] = 0. This observation is significant in the context of the BCJ duality conjecture, as referenced in the arXiv paper 1507.06288. The discussion also touches on the complexities of understanding the proof of Schouten's identity as presented in Srednicki's work.

PREREQUISITES
  • Understanding of Schouten identity and its applications in algebraic structures.
  • Familiarity with Jacobi identity and its role in mathematical physics.
  • Knowledge of BCJ duality conjecture and its implications in theoretical physics.
  • Ability to interpret mathematical proofs, particularly in the context of Srednicki's work.
NEXT STEPS
  • Research the proof of Schouten's identity as detailed in Srednicki's texts.
  • Explore the implications of the BCJ duality conjecture in particle physics.
  • Study the relationship between Schouten and Jacobi identities in advanced algebra.
  • Review the arXiv paper 1507.06288 for deeper insights into the discussion.
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This discussion is beneficial for theoretical physicists, mathematicians specializing in algebraic structures, and researchers exploring the BCJ duality conjecture.

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Am I the only one who sees the resemblance between these two identities?

Schouten:

<p q> <r s> +<p r> <s q>+ <p s > <q r> =0

Jacobi:

[A,[B,C]]+[C,[A,B]]+[B,[C,A]]=0

In Schouten the p occours in each term in the three terms, so we can regard it as dumby variable, and somehow get a correspondence between these two identities, or the algebraic structures that each identity is used in.

Am I being a cranck here? it's not my intention, as always, just trying to understand.

P.S
I am not sure I understand the proof of Schouten's identity in Srednicki's, I'll try to reread it.
 
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I had a dream or a thought about your work; any new progress on your work?
 
Well, for one thing, I'm investigating how it relates to BCJ duality.
 
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