Multilinear nilalgebras and the Jacobian theorem
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911189197389824 |
|---|---|
| author | Piontkovski, Dmitri |
| author_facet | Piontkovski, Dmitri |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02195 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multilinear nilalgebras and the Jacobian theorem Piontkovski, Dmitri Rings and Algebras Commutative Algebra Algebraic Geometry 17A42, 15A39, 14R15 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. |
| title | Multilinear nilalgebras and the Jacobian theorem |
| topic | Rings and Algebras Commutative Algebra Algebraic Geometry 17A42, 15A39, 14R15 |
| url | https://arxiv.org/abs/2510.02195 |