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http://hdl.handle.net/1942/30427
Title: | The Maximal Abelian Dimension of a Lie Algebra, Rentschler's Property and Milovanov's Conjecture | Authors: | OOMS, Alfons | Issue Date: | 2020 | Publisher: | Springer Netherlands | Source: | ALGEBRAS AND REPRESENTATION THEORY, 23(3), p. 963-999. | 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. | Keywords: | Maximal abelian dimension;· Rentschler’s property;· Complete Poisson commutative subalgebras;· Filiform Lie algebras;· Milovanov’s conjecture | Document URI: | http://hdl.handle.net/1942/30427 | ISSN: | 1386-923X | e-ISSN: | 1572-9079 | DOI: | 10.1007/s10468-019-09877-5 | ISI #: | WOS:000539035300021 | Rights: | Springer Nature B.V. 2019 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2021 |
Appears in Collections: | Research publications |
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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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