On the equivalence of Lie symmetries and group representations

M. J. Craddock, Anthony H Dooley

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We consider families of linear, parabolic PDEs in n dimensions which possess Liesymmetrygroups of dimension at least four. We identify the Liesymmetrygroups of these equations with the (2n+1)-dimensional Heisenberg group and SL(2,R). We then show that for PDEs of this type, the Liesymmetries may be regarded as global projective representations of the symmetrygroup. We construct explicit intertwining operators between the symmetries and certain classical projective representations of the symmetrygroups. Banach algebras of symmetries are introduced.
Original languageEnglish
Pages (from-to)621-653
Number of pages33
JournalJournal of Differential Equations
Volume249
Issue number3
Early online date3 Mar 2010
DOIs
Publication statusPublished - 1 Aug 2010

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