Schouten identity resembles Jacobi identity

[MathematicalPhysicist]

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.

 

[garrett]

You are not the only one. This observation is at the heart of the BCJ duality conjecture. See, for example, https://arxiv.org/abs/1507.06288

 

[MathematicalPhysicist]

I had a dream or a thought about your work; any new progress on your work?

 

[garrett]

Well, for one thing, I'm investigating how it relates to BCJ duality.