On the equivalence of Lie symmetries and group representations

Craddock, MJ; Dooley, AH

On the equivalence of Lie symmetries and group representations

Craddock, MJ Dooley, AH

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Publication Type:: Journal Article
Citation:: Journal of Differential Equations, 2010, 249 (3), pp. 621 - 653
Issue Date:: 2010-08-01

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Field	Value	Language
dc.contributor.author	Craddock, MJ	en_US
dc.contributor.author	Dooley, AH https://orcid.org/0000-0002-2656-3042	en_US
dc.date.issued	2010-08-01	en_US
dc.identifier.citation	Journal of Differential Equations, 2010, 249 (3), pp. 621 - 653	en_US
dc.identifier.issn	0022-0396	en_US
dc.identifier.uri	http://hdl.handle.net/10453/13015
dc.description.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{double-struck}). 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. © 2010 Elsevier Inc.	en_US
dc.relation.ispartof	Journal of Differential Equations	en_US
dc.relation.isbasedon	10.1016/j.jde.2010.02.003	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	On the equivalence of Lie symmetries and group representations	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	249	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0101 Pure Mathematics	en_US
dc.location.activity	ISI:000278873500007	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	open_access
pubs.issue	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	249	en_US

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{double-struck}). 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. © 2010 Elsevier Inc.

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http://hdl.handle.net/10453/13015