Comptes Rendus
no. 2
Algebra/Lie algebras
The groups of automorphisms of the Lie algebras of formally analytic vector fields with constant divergence

Presented by: the Editorial Board

Vladimir V. Bavula1
1 Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK
Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 85-88.

Let Sn=K[[x1,…,xn]] be the algebra of power series over a field K of characteristic zero, Snc be the group of continuous automorphisms of Sn with constant Jacobian, and Divnc be the Lie algebra of derivations of Sn with constant divergence. We prove that AutLie(Divnc)=AutLie,c(Divnc)≃Snc.

Soit Sn=K[[x1,…,xn]] lʼalgèbre des séries formelles sur un corps K de caractéristique zéro, Snc le groupe des automorphismes continus de Sn de jacobien constant et Divnc lʼalgèbre de Lie des dérivations de Sn à divergence constante. Nous montrons les identités AutLie(Divnc)=AutLie,c(Divnc)≃Snc.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.12.001

Vladimir V. Bavula 1

1 Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK 
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Vladimir V. Bavula. The groups of automorphisms of the Lie algebras of formally analytic vector fields with constant divergence. Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 85-88. doi : 10.1016/j.crma.2013.12.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.12.001/

[1] V.V. Bavula The groups of automorphisms of the Lie algebras of polynomial vector fields with zero or constant divergence | arXiv

[2] A.N. Rudakov Automorphism groups of infinite-dimensional simple Lie algebras, Izv. Akad. Nauk SSSR, Ser. Mat., Volume 33 (1969), pp. 748-764

[3] A.N. Rudakov Subalgebras and automorphisms of Lie algebras of Cartan type, Funkc. Anal. Prilozh., Volume 20 (1986) no. 1, pp. 83-84

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