We prove that the subgroup of triangular automorphisms of the complex affine -space is maximal among all solvable subgroups of for every . In particular, it is a Borel subgroup of , when the latter is viewed as an ind-group. In dimension two, we prove that the triangular subgroup is a maximal closed subgroup and that nevertheless, it is not maximal among all subgroups of . Given an automorphism of , we study the question whether the group generated by and the triangular subgroup is equal to the whole group .
Nous montrons que le sous-groupe des automorphismes triangulaires est un sous-groupe résoluble maximal de pour tout . Il forme ainsi un sous-groupe de Borel du ind-groupe . En dimension deux, nous montrons que le sous-groupe triangulaire est un sous-groupe fermé maximal mais qu’il n’est néanmoins pas maximal parmi tous les sous-groupes de . Un automorphisme de étant donné, nous étudions la question suivante : le sous-groupe engendré par et par les automorphismes triangulaires est-il égal au groupe tout entier ?
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Keywords: Polynomial automorphisms, triangular automorphisms, ind-groups
Mot clés : Automorphismes polynomiaux, automorphismes triangulaires, ind-groupes
@article{AIF_2018__68_1_393_0, author = {Furter, Jean-Philippe and Poloni, Pierre-Marie}, title = {On the maximality of the triangular subgroup}, journal = {Annales de l'Institut Fourier}, pages = {393--421}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {1}, year = {2018}, doi = {10.5802/aif.3165}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.3165/} }
TY - JOUR AU - Furter, Jean-Philippe AU - Poloni, Pierre-Marie TI - On the maximality of the triangular subgroup JO - Annales de l'Institut Fourier PY - 2018 SP - 393 EP - 421 VL - 68 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.3165/ DO - 10.5802/aif.3165 LA - en ID - AIF_2018__68_1_393_0 ER -
%0 Journal Article %A Furter, Jean-Philippe %A Poloni, Pierre-Marie %T On the maximality of the triangular subgroup %J Annales de l'Institut Fourier %D 2018 %P 393-421 %V 68 %N 1 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.3165/ %R 10.5802/aif.3165 %G en %F AIF_2018__68_1_393_0
Furter, Jean-Philippe; Poloni, Pierre-Marie. On the maximality of the triangular subgroup. Annales de l'Institut Fourier, Volume 68 (2018) no. 1, pp. 393-421. doi : 10.5802/aif.3165. http://archive.numdam.org/articles/10.5802/aif.3165/
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