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 $B$?

  • $\begingroup$ I deleted my answer, because the comment thread was becoming absurd. $\endgroup$ Aug 20, 2019 at 21:30


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