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Michael Albanese
Michael Albanese
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In thethis paper, page 149, the super Jacobi identity is given by \begin{align} J(x, y,z) := (-1)^{|x||z|}[[x, y],z] +(-1)^{|z||y|}[[z,x], y]+(-1)^{|y||x|}[[y,z],x] = 0. \end{align} But in thethis article, the super Jacobi identity is given by \begin{align} [x,[y,z]]=[[x,y],z]+(-1)^{|x| |y|}[y,[x,z]]. \end{align} Are these two definitions equivalent? Thank you very much.

In the paper, page 149, the super Jacobi identity is given by \begin{align} J(x, y,z) := (-1)^{|x||z|}[[x, y],z] +(-1)^{|z||y|}[[z,x], y]+(-1)^{|y||x|}[[y,z],x] = 0. \end{align} But in the article, the super Jacobi identity is given by \begin{align} [x,[y,z]]=[[x,y],z]+(-1)^{|x| |y|}[y,[x,z]]. \end{align} Are these two definitions equivalent? Thank you very much.

In this paper, page 149, the super Jacobi identity is given by \begin{align} J(x, y,z) := (-1)^{|x||z|}[[x, y],z] +(-1)^{|z||y|}[[z,x], y]+(-1)^{|y||x|}[[y,z],x] = 0. \end{align} But in this article, the super Jacobi identity is given by \begin{align} [x,[y,z]]=[[x,y],z]+(-1)^{|x| |y|}[y,[x,z]]. \end{align} Are these two definitions equivalent? Thank you very much.

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Michael Albanese
Michael Albanese
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Jianrong Li
Jianrong Li
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Two definitions of the super Jacobi identity

In the paper, page 149, the super Jacobi identity is given by \begin{align} J(x, y,z) := (-1)^{|x||z|}[[x, y],z] +(-1)^{|z||y|}[[z,x], y]+(-1)^{|y||x|}[[y,z],x] = 0. \end{align} But in the article, the super Jacobi identity is given by \begin{align} [x,[y,z]]=[[x,y],z]+(-1)^{|x| |y|}[y,[x,z]]. \end{align} Are these two definitions equivalent? Thank you very much.