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Automorphisms of Lie Algebras.

Gray, Robert James. (2013) Automorphisms of Lie Algebras. Doctoral thesis, University of Surrey (United Kingdom)..

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Abstract

Discrete symmetries of differential equations can be calculated systematically, using an indirect method that involves classifying Lie algebra automorphisms. With this in mind, we classify the automorphisms of all six-dimensional real indecomposable Lie algebras. Almost every automorphism group is recorded in a one-line table entry from which inner and outer automorphisms, exponentiated derivations and discrete automorphisms can be identified easily. Naturally, constraints on the form of a differential equation’s Lie groups of point symmetries make them easier to calculate. For instance, it is known that the Lie groups of point symmetries of linear scalar partial differential equations of order two or more are projectable, and that the transforms of the dependent variables are linear in the original dependent variables. We generalize this result to systems of linear differential equations in Kovalevskaya form, then use it to investigate the structure of their (generally infinitedimensional) Lie point symmetry algebras. For example, we prove that the generators of linear superposition symmetries span the maximal abelian ideal. These results are used to simplify the classification of Lie symmetry algebra automorphisms, and to simplify the related problem of calculating discrete point symmetries. Generalizations to linearizable systems are given.

Item Type: Thesis (Doctoral)
Divisions : Theses
Authors : Gray, Robert James.
Date : 2013
Additional Information : Thesis (Ph.D.)--University of Surrey (United Kingdom), 2013.
Depositing User : EPrints Services
Date Deposited : 24 Apr 2020 15:26
Last Modified : 24 Apr 2020 15:26
URI: http://epubs.surrey.ac.uk/id/eprint/855222

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