Projectable Lie algebras of vector fields in 3D

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2018Embargo end date: 01 Mar 2018 Norway English Publisher:Elsevier BVJournal:Journal of Geometry and Physics, volume 132, pages 222-229 (issn: 0393-0440,

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Authors: Eivind Schneider;

doi: 10.1016/j.geomphys.2018.05.025 , 10.48550/arxiv.1803.08878

arXiv: 1803.08878

handle: 10037/14569

Projectable Lie algebras of vector fields in 3D

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Abstract

Starting with Lie's classification of finite-dimensional transitive Lie algebras of vector fields on $\mathbb C^2$ we construct Lie algebras of vector fields on the bundle $\mathbb C^2 \times \mathbb C$ by lifting the Lie algebras from the base. There are essentially three types of transitive lifts and we compute all of them for the Lie algebras from Lie's classification. The simplest type of lift is encoded by Lie algebra cohomology.

Country

Norway

Related Organizations

Norwegian Association of Higher Education Institutions
Norway
The Arctic University of Norway
Norway

Keywords

Mathematics - Differential Geometry, Lie algebras of vector fields and related (super) algebras, Transformation groups, transformation groups, Cohomology of Lie (super)algebras, Lie algebra cohomology, 17B66, 17B56, 57S25, Differential Geometry (math.DG), Lie algebras of vector fields, VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Algebra/algebraisk analyse: 414, FOS: Mathematics, VDP::Mathematics and natural science: 400::Mathematics: 410::Algebra/algebraic analysis: 414, Groups acting on specific manifolds

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