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Let $(L,.)$ be a Lie superalgebra endowed with an even supersymmetric non-degenerate and invariant bilinear form $B$ (i.e $(L,.,B)$ is a quadratic Lie superalgebra). If we have the equality $B(x,y.z)=(-1)^{\vert x\vert +\vert y\vert +\vert z\vert }B(x,z.y)$, what can we conclude using the non-degeneracy of $B$?

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  • $\begingroup$ I deleted my answer, because the comment thread was becoming absurd. $\endgroup$ – José Figueroa-O'Farrill Aug 20 '19 at 21:30

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