Multilinear nilalgebras and the Jacobian theorem
Rings and Algebras
2025-10-03 v1 Commutative Algebra
Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.2510.02195,
title = {Multilinear nilalgebras and the Jacobian theorem},
author = {Dmitri Piontkovski},
journal= {arXiv preprint arXiv:2510.02195},
year = {2025}
}
Comments
3 pp