Eastwood, Michael; Leistner, Thomas Higher symmetries of the square of the Laplacian. (English) Zbl 1137.58014 Eastwood, Michael (ed.) et al., Symmetries and overdetermined systems of partial differential equations. Proceedings of the IMA summer program, Minneapolis, MN, USA, July 17–August 4, 2006. New York, NY: Springer (ISBN 978-0-387-73830-7/hbk). The IMA Volumes in Mathematics and its Applications 144, 319-338 (2008). Summary: The symmetry operators for the Laplacian in flat space were recently described and here we consider the same question for the square of the Laplacian. Again, there is a close connection with conformal geometry. There are three main steps in our construction. The first is to show that the symbol of a symmetry is constrained by an overdetermined partial differential equation. The second is to show existence of symmetries with specified symbol (using a simple version of the AdS/CFT correspondence). The third is to compute the composition of two first order symmetry operators and hence determine the structure of the symmetry algebra. There are some interesting differences as compared to the corresponding results for the Laplacian.For the entire collection see [Zbl 1126.35005]. Cited in 18 Documents MSC: 58J70 Invariance and symmetry properties for PDEs on manifolds 16S35 Twisted and skew group rings, crossed products 53A30 Conformal differential geometry (MSC2010) 70S10 Symmetries and conservation laws in mechanics of particles and systems Keywords:conformal geometry × Cite Format Result Cite Review PDF Full Text: arXiv