Poisson deleting derivations algorithm: Poisson birational equivalence and Poisson spectrum.

Cesar Lecoutre (University of Glasgow)

Thursday 4th June, 2015 16:00-17:00 Maths 516

Abstract

We present a method, the so-called Poisson deleting derivations algorithm, to study a class P of polynomial Poisson algebras over an arbitrary field. We give two applications of the Poisson deleting derivations algorithm. Firstly we show that an algebra of the class P satisfies the quadratic Poisson Gel'fand-Kirillov problem, that is its field of fractions is isomorphic to the field of fractions of a Poisson affine space (a polynomial algebra where the Poisson bracket of two generators is equal to (a scalar multiple of) their product). Secondly we show how the algorithm help us to understand better the Poisson spectrum of a Poisson algebra of the class P. In particular we will show how the Poisson spectrum of the matrix Poisson variety can be understood combinatorially.

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