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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/23560

Title: The polynomiality of the Poisson center and semi-center of a Lie algebra and Dixmier's fourth problem
Authors: Ooms, Alfons
Issue Date: 2017
Citation: JOURNAL OF ALGEBRA, 477, p. 95-146
Abstract: Let g be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero. We provide necessary and also some sufficient conditions in order for its Poisson center and semi-center to be polynomial algebras over k. This occurs for instance if g is quadratic of index 2 with [g, g] = g and also if g is nilpotent of index at most 2. The converse holds for filiform Lie algebras of type Ln, Qn, Rn and Wn. We show how Dixmier’s fourth problem for an algebraic Lie algebra g can be reduced to that of its canonical truncation gΛ. Moreover, Dixmier’s statement holds for all Lie algebras of dimension at most eight. The nonsolvable ones among them possess a polynomial Poisson center and semi-center.
Notes: Ooms, AI (reprint author), Hasselt Univ, Dept Math, Agoralaan, Campus Diepenbeek, B-3590 Diepenbeek, Belgium. alfons.ooms@uhasselt.be
URI: http://hdl.handle.net/1942/23560
DOI: 10.1016/j.jalgebra.2016.12.009
ISI #: 000396380500006
ISSN: 0021-8693
Category: A1
Type: Journal Contribution
Appears in Collections: Research publications

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