Vol. 10, No. 5, 2016

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ISSN: 1944-7833 (e-only)
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Conjugacy classes of special automorphisms of the affine spaces

Jérémy Blanc

Vol. 10 (2016), No. 5, 939–967
Abstract

In the group of polynomial automorphisms of the plane, the conjugacy class of an element is closed if and only if the element is diagonalisable. In this article, we show that this does not hold for the group of special automorphisms, giving a first step in the direction of showing that this group is not simple, as an infinite-dimensional algebraic group.

Keywords
plane automorphisms, conjugacy classes, topology
Mathematical Subject Classification 2010
Primary: 14R10
Secondary: 14R20
Milestones
Received: 2 January 2015
Revised: 4 November 2015
Accepted: 4 March 2016
Published: 28 July 2016
Authors
Jérémy Blanc
Mathematisches Institut
Universität Basel
Spiegelgasse 1
CH-4051 Basel
Switzerland