A simple proof of Nowicki's conjecture on the kernel of an elementary derivation (Q841452)
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scientific article; zbMATH DE number 5604246
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simple proof of Nowicki's conjecture on the kernel of an elementary derivation |
scientific article; zbMATH DE number 5604246 |
Statements
A simple proof of Nowicki's conjecture on the kernel of an elementary derivation (English)
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16 September 2009
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Nowicki's conjecture is the following: define the derivation \(D:=y_1\partial_{x_1}+y_2\partial_{x_2}+\cdots+y_n\partial_{x_n}\) on \(k[x_1,\dots,x_n,y_1,\dots,y_n]\). Then its kernel is generated by the \(x_iy_j-x_jy_i\). The conjecture is surprisingly difficult to prove, and was open for a few years. The author gives a simple proof of 2.5 pages.
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locally nilpotent derivations
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kernel of derivation
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