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http://hdl.handle.net/1942/30427
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DC Field | Value | Language |
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dc.contributor.author | OOMS, Alfons | - |
dc.date.accessioned | 2020-01-30T10:05:35Z | - |
dc.date.available | 2020-01-30T10:05:35Z | - |
dc.date.issued | 2020 | - |
dc.date.submitted | 2020-01-30T09:18:43Z | - |
dc.identifier.citation | ALGEBRAS AND REPRESENTATION THEORY, 23(3), p. 963-999. | - |
dc.identifier.issn | 1386-923X | - |
dc.identifier.uri | http://hdl.handle.net/1942/30427 | - |
dc.description.abstract | A finite dimensional Lie algebra L with magic number c(L) is said to satisfy Rentschler's property if it admits an abelian Lie subalgebra H of dimension at least c(L) − 1. We study the occurrence of this new property in various Lie algebras, such as nonsolvable, solvable, nilpotent, metabelian and filiform Lie algebras. Under some mild condition H gives rise to a complete Poisson commutative subalgebra of the symmetric algebra S(L). Using this, we show that Milovanov's conjecture holds for the filiform Lie algebras of type L n , Q n , R n , W n and also for all filiform Lie algebras of dimension at most eight. For the latter the Poisson center of these Lie algebras is determined. | - |
dc.description.sponsorship | We would like to thank Rudolf Rentschler for his inspiring observation and for his helpful comments. We are also very grateful to Manuel Ceballos for his kind offer to compute α(L8,16) and α(L8,18) with his algorithm. Furthermore, we thank Alexander Elashvili for suggesting to include the metabelian case. Finally, we wish to thank Viviane Mebis for her excellent typing of the manuscript. | - |
dc.language.iso | en | - |
dc.publisher | Springer Netherlands | - |
dc.rights | Springer Nature B.V. 2019 | - |
dc.subject.other | Maximal abelian dimension | - |
dc.subject.other | · Rentschler’s property | - |
dc.subject.other | · Complete Poisson commutative subalgebras | - |
dc.subject.other | · Filiform Lie algebras | - |
dc.subject.other | · Milovanov’s conjecture | - |
dc.title | The Maximal Abelian Dimension of a Lie Algebra, Rentschler's Property and Milovanov's Conjecture | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 999 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 963 | - |
dc.identifier.volume | 23 | - |
local.format.pages | 37 | - |
local.bibliographicCitation.jcat | A1 | - |
local.publisher.place | VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.1007/s10468-019-09877-5 | - |
dc.identifier.isi | WOS:000539035300021 | - |
dc.identifier.eissn | 1572-9079 | - |
local.provider.type | CrossRef | - |
local.uhasselt.uhpub | yes | - |
local.uhasselt.international | no | - |
item.validation | ecoom 2021 | - |
item.fullcitation | OOMS, Alfons (2020) The Maximal Abelian Dimension of a Lie Algebra, Rentschler's Property and Milovanov's Conjecture. In: ALGEBRAS AND REPRESENTATION THEORY, 23(3), p. 963-999.. | - |
item.accessRights | Open Access | - |
item.contributor | OOMS, Alfons | - |
item.fulltext | With Fulltext | - |
crisitem.journal.issn | 1386-923X | - |
crisitem.journal.eissn | 1572-9079 | - |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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1802.07951.pdf | Peer-reviewed author version | 267.29 kB | Adobe PDF | View/Open |
Ooms2019_Article_TheMaximalAbelianDimensionOfAL.pdf Restricted Access | Published version | 612.09 kB | Adobe PDF | View/Open Request a copy |
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