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2011 The Lie Group in Infinite Dimension
V. Tryhuk, V. Chrastinová, O. Dlouhý
Abstr. Appl. Anal. 2011(SI1): 1-35 (2011). DOI: 10.1155/2011/919538


A Lie group acting on finite-dimensional space is generated by its infinitesimal transformations and conversely, any Lie algebra of vector fields in finite dimension generates a Lie group (the first fundamental theorem). This classical result is adjusted for the infinite-dimensional case. We prove that the (local, C smooth) action of a Lie group on infinite-dimensional space (a manifold modelled on ) may be regarded as a limit of finite-dimensional approximations and the corresponding Lie algebra of vector fields may be characterized by certain finiteness requirements. The result is applied to the theory of generalized (or higher-order) infinitesimal symmetries of differential equations.


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V. Tryhuk. V. Chrastinová. O. Dlouhý. "The Lie Group in Infinite Dimension." Abstr. Appl. Anal. 2011 (SI1) 1 - 35, 2011.


Published: 2011
First available in Project Euclid: 12 August 2011

zbMATH: 1223.22018
MathSciNet: MR2771243
Digital Object Identifier: 10.1155/2011/919538

Rights: Copyright © 2011 Hindawi

Vol.2011 • No. SI1 • 2011
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