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Poisson brackets and Poisson spectra in polynomial algebras. (English) Zbl 1273.17027
Ara, P. (ed.) et al., New trends in noncommutative algebra. A conference in honor of Ken Goodearl’s 65th birthday, Washington, Seattle, WA, USA, August 9–14, 2010. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-5297-2). Contemporary Mathematics 562, 169-187 (2012).
Summary: Poisson brackets on the polynomial algebra $$\mathbb C[x,y,z]$$ are studied. A description of all such brackets is given and, for a significant class of Poisson brackets, the Poisson prime ideals and Poisson primitive ideals are determined. The results are illustrated by numerous examples.
For the entire collection see [Zbl 1232.16001].

##### MSC:
 17B63 Poisson algebras 13N15 Derivations and commutative rings 16S36 Ordinary and skew polynomial rings and semigroup rings 16W25 Derivations, actions of Lie algebras
##### Keywords:
Poisson algebra; Poisson prime ideal; polynomial algebra
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