Every monomorphism of the Lie algebra of triangular polynomial derivations is an automorphism

Bavula, Vladimir V.

doi:10.1016/j.crma.2012.06.001

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]

Présenté par : the Editorial Board

Bavula, Vladimir V.¹

¹ Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK

Comptes Rendus. Mathématique, Tome 350 (2012) no. 11-12, pp. 553-556.

Résumé
Abstract

Nous montrons que tout homomorphisme injectif de lʼalgèbre de Lie $u_{n}$ des dérivations triangulaires de lʼalgèbre de polynômes $P_{n} = K [x_{1}, \dots, x_{n}]$ est un automorphisme.

We prove that every monomorphism of the Lie algebra $u_{n}$ of triangular derivations of the polynomial algebra $P_{n} = K [x_{1}, \dots, x_{n}]$ is an automorphism.

Reçu le : 2012-05-23
Accepté le : 2012-06-08
Publié le : 2012-06-01

DOI : 10.1016/j.crma.2012.06.001

Affiliations des auteurs :

Bavula, Vladimir V. ¹

¹ Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK

@article{CRMATH_2012__350_11-12_553_0,
     author = {Bavula, Vladimir V.},
     title = {Every monomorphism of the {Lie} algebra of triangular polynomial derivations is an automorphism},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {553--556},
     publisher = {Elsevier},
     volume = {350},
     number = {11-12},
     year = {2012},
     doi = {10.1016/j.crma.2012.06.001},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2012.06.001/}
}

TY  - JOUR
AU  - Bavula, Vladimir V.
TI  - Every monomorphism of the Lie algebra of triangular polynomial derivations is an automorphism
JO  - Comptes Rendus. Mathématique
PY  - 2012
SP  - 553
EP  - 556
VL  - 350
IS  - 11-12
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2012.06.001/
DO  - 10.1016/j.crma.2012.06.001
LA  - en
ID  - CRMATH_2012__350_11-12_553_0
ER  -

%0 Journal Article
%A Bavula, Vladimir V.
%T Every monomorphism of the Lie algebra of triangular polynomial derivations is an automorphism
%J Comptes Rendus. Mathématique
%D 2012
%P 553-556
%V 350
%N 11-12
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2012.06.001/
%R 10.1016/j.crma.2012.06.001
%G en
%F CRMATH_2012__350_11-12_553_0

Bavula, Vladimir V. Every monomorphism of the Lie algebra of triangular polynomial derivations is an automorphism. Comptes Rendus. Mathématique, Tome 350 (2012) no. 11-12, pp. 553-556. doi : 10.1016/j.crma.2012.06.001. http://www.numdam.org/articles/10.1016/j.crma.2012.06.001/

Bibliographie
Cité par

[1] Bavula, V.V. The Jacobian Conjecture_2n implies the Dixmier Problem_n | arXiv

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

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

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

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

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

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

Cité par Sources :