Comptes Rendus
Algebra/Lie Algebras
Every monomorphism of the Lie algebra of triangular polynomial derivations is an automorphism
[Tout homomorphisme injectif de lʼalgèbre de Lie des dérivations triangulaires polynomiales est un automorphisme]
Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 553-556.

Nous montrons que tout homomorphisme injectif de lʼalgèbre de Lie un des dérivations triangulaires de lʼalgèbre de polynômes Pn=K[x1,,xn] est un automorphisme.

We prove that every monomorphism of the Lie algebra un of triangular derivations of the polynomial algebra Pn=K[x1,,xn] is an automorphism.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.06.001

Vladimir V. Bavula 1

1 Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK
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     title = {Every monomorphism of the {Lie} algebra of triangular polynomial derivations is an automorphism},
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Vladimir V. Bavula. Every monomorphism of the Lie algebra of triangular polynomial derivations is an automorphism. Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 553-556. doi : 10.1016/j.crma.2012.06.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.06.001/

[1] V.V. Bavula The Jacobian Conjecture2n implies the Dixmier Problemn | arXiv

[2] V.V. Bavula An analogue of the Conjecture of Dixmier is true for the algebra of polynomial integro-differential operators | arXiv

[3] V.V. Bavula Lie algebras of unitriangular polynomial derivations and an isomorphism criterion for their Lie factor algebras | arXiv

[4] V.V. Bavula The groups of automorphisms of the Lie algebras of unitriangular polynomial derivations | arXiv

[5] A. Belov-Kanel; M. Kontsevich The Jacobian Conjecture is stably equivalent to the Dixmier Conjecture, Mosc. Math. J., Volume 7 (2007) no. 2, pp. 209-218 | arXiv

[6] J. Dixmier Sur les algèbres de Weyl, Bull. Soc. Math. France, Volume 96 (1968), pp. 209-242

[7] Y. Tsuchimoto Endomorphisms of Weyl algebra and p-curvatures, Osaka J. Math., Volume 42 (2005) no. 2, pp. 435-452

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