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Transitive Lie Algebras of Nilpotent Vector Fields and their Tanaka Prolongations

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dc.abstract.enTransitive nilpotent local Lie algebras of vector fields can be easily constructed from dilations h of Rn with positive weights (give me a sequence of n positive integers and I will give you a transitive nilpotent Lie algebra of vector fields on Rn ) as the Lie algebras g<0(h) of the polynomial vector fields of negative weights with respect to h. We provide a condition for the dilation h such that the Lie algebras of polynomial vectors defined by h are exactly the Tanaka prolongations of the corresponding nilpotent Lie algebras g<0(h) . However, in some cases of dilations h we can find some ‘strange’ elements of the Tanaka prolongations of g<0(h) , which we describe in detail. In particular, we give a complete description of derivations of degree 0 for the Lie algebra g<0(h) .
dc.affiliationUniwersytet Warszawski
dc.contributor.authorGrabowska, Katarzyna
dc.contributor.authorGrabowski, Janusz
dc.contributor.authorRavanpak, Zohreh
dc.date.accessioned2024-01-26T11:05:21Z
dc.date.available2024-01-26T11:05:21Z
dc.date.issued2021
dc.description.financePublikacja bezkosztowa
dc.description.volume31
dc.identifier.issn0949-5932
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/123717
dc.identifier.weblinkhttps://www.heldermann.de/JLT/JLT31/JLT314/jlt31051.htm
dc.languageeng
dc.pbn.affiliationphysical sciences
dc.relation.ispartofJournal of Lie Theory
dc.relation.pages1003-1014
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.enVector field
dc.subject.ennilpotent Lie algebra
dc.subject.endilation
dc.subject.enderivation
dc.subject.enhomogeneity structures
dc.titleTransitive Lie Algebras of Nilpotent Vector Fields and their Tanaka Prolongations
dc.typeJournalArticle
dspace.entity.typePublication