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|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.
|ISI #: ||000396380500006|
|Type: ||Journal Contribution|
|Appears in Collections: ||Research publications|
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|Published version||743.79 kB||Adobe PDF|
|Peer-reviewed author version||395.92 kB||Adobe PDF|
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