标题： 多重线性幂零代数和雅可比定理 显示英文标题

标题： Multilinear nilalgebras and the Jacobian theorem

摘要： 如果对称多重线性代数是弱幂零的，那么它是Engel。 这个结果可以看作是众所周知的雅可比定理的无限维类似物，该定理指出，如果一个多项式映射有多项式逆，则其雅可比矩阵是可逆的。 这改进了Gerstenhaber的一个定理，并部分回答了Dotsenko提出的问题。 显示英文摘要

摘要： 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.