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http://hdl.handle.net/1942/34195
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DC Field | Value | Language |
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dc.contributor.author | OOMS, Alfons | - |
dc.date.accessioned | 2021-06-02T09:15:23Z | - |
dc.date.available | 2021-06-02T09:15:23Z | - |
dc.date.issued | 2022 | - |
dc.date.submitted | 2021-04-22T09:32:48Z | - |
dc.identifier.citation | ALGEBRAS AND REPRESENTATION THEORY, 25(3), p. 561-579 | - |
dc.identifier.uri | http://hdl.handle.net/1942/34195 | - |
dc.description.abstract | Let g be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero. Denote by U(g) its enveloping algebra with quotient division ring D(g). In 1974, at the end of his book "Algèbres enveloppantes", Jacques Dixmier listed 40 open problems, of which the fourth one asked if the center Z(D(g)) is always a purely transcendental extension of k. We show this is the case if g is algebraic whose Poisson semi-center Sy(g) is a polynomial algebra over k. This can be applied to many biparabolic (seaweed) subalgebras of semi-simple Lie algebras. We also provide a survey of Lie algebras for which Dixmier's problem is known to have a positive answer. This includes all Lie algebras of dimension at most 8. We prove this is also true for all 9-dimensional algebraic Lie algebras. Finally, we improve the statement of Theorem 53 of Ooms (J. Algebra 477, 95-146, 2017). | - |
dc.description.sponsorship | We would like to thank Michel Van den Bergh for some helpful discussions and for providing Proposition 3.1. We are also grateful to Vladimir Popov for accurately describing the relevant results (and their references) of Katsylo and Bogomolov. Finally we wish to thank Viviane Mebis for the excellent typing of the manuscript. | - |
dc.language.iso | en | - |
dc.publisher | SPRINGER | - |
dc.rights | The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature 2021 | - |
dc.subject.other | Dixmier's fourth problem | - |
dc.subject.other | Poisson semi-center | - |
dc.subject.other | Biparabolic subalgebras | - |
dc.title | On Dixmier’s Fourth Problem | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 579 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 561 | - |
dc.identifier.volume | 25 | - |
local.format.pages | 19 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | Ooms, AI (corresponding author), Hasselt Univ, Dept Math, Campus Diepenbeek, B-3590 Diepenbeek, Belgium. | - |
dc.description.notes | alfons.ooms@uhasselt.be | - |
dc.description.other | Ooms, AI (corresponding author), Hasselt Univ, Dept Math, Campus Diepenbeek, B-3590 Diepenbeek, Belgium. alfons.ooms@uhasselt.be | - |
local.publisher.place | VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.1007/s10468-021-10035-z | - |
dc.identifier.isi | WOS:000626374300001 | - |
local.provider.type | wosris | - |
local.uhasselt.uhpub | yes | - |
local.description.affiliation | [Ooms, Alfons I.] Hasselt Univ, Dept Math, Campus Diepenbeek, B-3590 Diepenbeek, Belgium. | - |
local.uhasselt.international | no | - |
item.contributor | OOMS, Alfons | - |
item.validation | ecoom 2022 | - |
item.fulltext | With Fulltext | - |
item.fullcitation | OOMS, Alfons (2022) On Dixmier’s Fourth Problem. In: ALGEBRAS AND REPRESENTATION THEORY, 25(3), p. 561-579. | - |
item.accessRights | Restricted Access | - |
crisitem.journal.issn | 1386-923X | - |
crisitem.journal.eissn | 1572-9079 | - |
Appears in Collections: | Research publications |
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s10468-021-10035-z.pdf Restricted Access | Published version | 408.71 kB | Adobe PDF | View/Open Request a copy |
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