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Title: The Poisson center and polynomial, maximal Poisson commutative subalgebras, especially for nilpotent Lie algebras of dimension at most seven
Authors: OOMS, Alfons 
Issue Date: 2012
Source: JOURNAL OF ALGEBRA, 365, p. 83-113
Abstract: Let g be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero. We collect some general results on the Poisson center of S(g), including some simple criteria regarding its polynomiality, and also on certain Poisson commutative subalgebras of S(g). These facts are then used to finish our earlier work on this subject, i.e. to give an explicit description for the Poisson center of all indecomposable, nilpotent Lie algebras of dimension at most seven. Among other things, we also provide a polynomial, maximal Poisson commutative subalgebra of S(g), enjoying additional properties. As a by-product we show that a conjecture by Milovanov is valid in this situation. These results easily carry over to the enveloping algebra U(g).
Keywords: Poisson center; Poisson commutative subalgebra; Nilpotent Lie algebra; Enveloping algebra
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ISSN: 0021-8693
e-ISSN: 1090-266X
DOI: 10.1016/j.jalgebra.2012.04.029
ISI #: 000305776900006
Rights: 2012 Elsevier Inc. All rights reserved
Category: A1
Type: Journal Contribution
Validations: ecoom 2013
Appears in Collections:Research publications

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