Comptes Rendus
no. 11-12
Algebra/Lie Algebras
Every monomorphism of the Lie algebra of triangular polynomial derivations is an automorphism
the Editorial Board
Vladimir V. Bavula1
1Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK
Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 553-556

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

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.

Received:
Accepted:
Published online:
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 
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
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[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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