Symmetry via Lie algebra cohomology

2010/06/08 by Michael Eastwood, Eastwood, Michael
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1006.1671

openalex publication_date 2010/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Killing operator on a Riemannian manifold is a linear differential operator on vector fields whose kernel provides the infinitesimal Riemannian symmetries. The Killing operator is best understood in terms of its prolongation, which entails some simple tensor identities. These simple identities can be viewed as arising from the identification of certain Lie algebra cohomologies. The point is that this case provides a model for more complicated operators similarly concerned with symmetry.

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