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On the equivalence of Lie symmetries and group representations
Authors:MJ Craddock  AH Dooley
Institution:a Department of Mathematical Sciences, University of Technology Sydney, PO Box 123, Broadway, NSW 2007, Australia
b School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia
Abstract:We consider families of linear, parabolic PDEs in n dimensions which possess Lie symmetry groups of dimension at least four. We identify the Lie symmetry groups of these equations with the (2n+1)-dimensional Heisenberg group and SL(2,R). We then show that for PDEs of this type, the Lie symmetries may be regarded as global projective representations of the symmetry group. We construct explicit intertwining operators between the symmetries and certain classical projective representations of the symmetry groups. Banach algebras of symmetries are introduced.
Keywords:
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