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Multilinear nilalgebras and the Jacobian theorem
Dmitri Piontkovski
https://arxiv.org/abs/2510.02195 https://arxiv.org/pdf/2510.02195

Multilinear nilalgebras and the Jacobian theorem
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed by Dotsenko.