Casimir elements of polynomial ring derivations (in Ukrainian)

L.P.Bedratyuk

Let $k[X]{:=}\,k[x_1,\ldots ,x_n]$ be a polynomial algebra over a field $k$ of characteristic zero. We offer a general description of a kernel of an arbitrary polynomial derivation $D$ by using a construction which is a commutative analogue of a construction of Casimir elements of Lie algebras of finite dimension.

1. Nowicki A. Polynomial derivation and their Ring of Constants. -- UMK: Torun,1994.

2. van den Essen A. Polynomial automorphisms and the Jacobian conjecture/ Progress in Mathematics.-- V.190. -- Basel, 2000.

3. Freudenburg G. A survey of counterexamples to Hilbert's fourteenth problem// Serdica Math. J.-- 2001.-- P.171--192.

4. Дискмье Ж. Универсальные обертывающие алгебры. -- М.: Мир, 1978. -- 408~c.

5. Daigle D., Freudenburg G. A couterexample to Hilbert's fourtheenth problem in dimension five// J. of Algebra. -- 1999. -- V. 221. -- P. 528--535.

6. Rentschler R. Opérations du groupe additif sur le plan affine// C.R. Acad. Sc., Paris.-- 1968.-- V.267. P.384--387.

	Casimir elements of polynomial ring derivations (in Ukrainian)
Author	L.P.Bedratyuk bedratyuk@ief.tup.km.ua, leonid.uk@gmail.com Khmelnytskyi National University
Abstract	Let $k[X]{:=}\,k[x_1,\ldots ,x_n]$ be a polynomial algebra over a field $k$ of characteristic zero. We offer a general description of a kernel of an arbitrary polynomial derivation $D$ by using a construction which is a commutative analogue of a construction of Casimir elements of Lie algebras of finite dimension.
Keywords	kernel, polynomial derivation, Casimir element, Lie algebra
DOI	doi:10.30970/ms.27.2.115-119
Reference	1. Nowicki A. Polynomial derivation and their Ring of Constants. -- UMK: Torun,1994. 2. van den Essen A. Polynomial automorphisms and the Jacobian conjecture/ Progress in Mathematics.-- V.190. -- Basel, 2000. 3. Freudenburg G. A survey of counterexamples to Hilbert's fourteenth problem// Serdica Math. J.-- 2001.-- P.171--192. 4. Дискмье Ж. Универсальные обертывающие алгебры. -- М.: Мир, 1978. -- 408~c. 5. Daigle D., Freudenburg G. A couterexample to Hilbert's fourtheenth problem in dimension five// J. of Algebra. -- 1999. -- V. 221. -- P. 528--535. 6. Rentschler R. Opérations du groupe additif sur le plan affine// C.R. Acad. Sc., Paris.-- 1968.-- V.267. P.384--387.
Pages	115-119
Volume	27
Issue	2
Year	2007
Journal	Matematychni Studii
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