Conjugacy classes of special automorphisms of the affine spaces

Blanc, Jérémy

doi:10.2140/ant.2016.10.939

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Conjugacy classes of special automorphisms of the affine spaces

Jérémy Blanc

Vol. 10 (2016), No. 5, 939–967

DOI: 10.2140/ant.2016.10.939

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

Vol. 10, No. 5, 2016