On plane polynomial automorphisms commuting with simple derivations
Commutative Algebra
2016-06-20 v2
Abstract
We consider the subgroup Aut(D) consisting of automorphisms of K[x,y] commuting with a derivation D, where K is an algebraically closed field of characteristic 0. We prove that if D is simple (i.e. D does not stabilize non-trivial ideals), then Aut(D)=1, in the case where D is of Shamsuddin type this result was proven by R.Baltazar in 2014 (arXiv:1412.8373). Moreover, we describe Aut(D) for Shamsuddin type derivations and deduce that Aut(D)=1 for a general such derivation implies D is simple.
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Cite
@article{arxiv.1604.04933,
title = {On plane polynomial automorphisms commuting with simple derivations},
author = {Luís Gustavo Mendes and Ivan Pan},
journal= {arXiv preprint arXiv:1604.04933},
year = {2016}
}
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9 pages