On weakly semisimple derivations of the polynomial ring in two variables
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On weakly semisimple derivations of the polynomial ring in two variables
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| Creator |
Gavran, V.S.
Stepukh, V.V. |
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| Description |
Let K be an algebraically closed field of characteristic zero and K[x, y] the polynomial ring. Every element f ∈ K[x, y] determines the Jacobian derivation Df of K[x, y] by the rule Df(h) = detJ(f, h), where J(f, h) is the Jacobian matrix of the polynomials f and h. A polynomial f is called weakly semisimple if there exists a polynomial g such that Df(g) = λg for some nonzero λ ∈ K. Ten years ago, Y. Stein posed a problem of describing all weakly semisimple polynomials (such a description would characterize all two dimensional nonabelian subalgebras of the Lie algebra of all derivations of K[x, y] with zero divergence). We give such a description for polynomials f with the separated variables, i.e. which are of the form: f(x, y) = f₁(x)f₂(y) for some f₁(t), f₂(t) ∈ K[t].
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| Date |
2019-06-14T03:25:55Z
2019-06-14T03:25:55Z 2014 |
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| Type |
Article
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| Identifier |
On weakly semisimple derivations of the polynomial ring in two variables / V.S. Gavran, V.V. Stepukh // Algebra and Discrete Mathematics. — 2014. — Vol. 18, № 1. — С. 50–58. — Бібліогр.: 7 назв. — англ.
1726-3255 2010 MSC:13N15; 13N99. http://dspace.nbuv.gov.ua/handle/123456789/153346 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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