The Maximal Abelian Dimension of a Lie Algebra, Rentschler’s Property and Milovanov’s Conjecture View Full Text


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Article Info

DATE

2019-03-20

AUTHORS

Alfons I. Ooms

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 Ln, Qn, Rn, Wn and also for all filiform Lie algebras of dimension at most eight. For the latter the Poisson center of these Lie algebras is determined. More... »

PAGES

1-37

Journal

TITLE

Algebras and Representation Theory

ISSUE

N/A

VOLUME

N/A

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10468-019-09877-5

DOI

http://dx.doi.org/10.1007/s10468-019-09877-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112896825


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