Log-Canonical Coordinates for Poisson Brackets and Rational Changes of Coordinates
Rings and Algebras
2017-10-23 v1
Abstract
Goodearl and Launois have shown that for a log-canonical Poisson bracket on affine space there is no rational change of coordinates for which the Poisson bracket is constant. Our main result is that if affine space is given a log-canonical Poisson bracket, then there does not exist any rational change of coordinates for which the Poisson bracket is linear. Hence, log-canonical coordinates can be thought of as the simplest possible algebraic coordinates for affine space with a log-canonical coordinate system. In proving this conjecture we find certain invariants of log-canonical Poisson brackets on affine space which linear Poisson brackets do not have.
Cite
@article{arxiv.1703.06521,
title = {Log-Canonical Coordinates for Poisson Brackets and Rational Changes of Coordinates},
author = {John Machacek and Nicholas Ovenhouse},
journal= {arXiv preprint arXiv:1703.06521},
year = {2017}
}