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arXiv · 1703.06521

Log-Canonical Coordinates for Poisson Brackets and Rational Changes of Coordinates

John Machacek·Nicholas Ovenhouse
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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.

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John Machacek, Nicholas Ovenhouse. 2017-03-19. Log-Canonical Coordinates for Poisson Brackets and Rational Changes of Coordinates. https://doi.org/10.1016/j.geomphys.2017.07.023

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