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- W2037083588 abstract "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,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msup><mml:mi>C</mml:mi><mml:mi>∞</mml:mi></mml:msup></mml:math>smooth) action of a Lie group on infinite-dimensional space (a manifold modelled on<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msup><mml:mi>ℝ</mml:mi><mml:mi>∞</mml:mi></mml:msup></mml:math>) 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." @default.
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- W2037083588 date "2011-01-01" @default.
- W2037083588 modified "2023-09-24" @default.
- W2037083588 title "The Lie Group in Infinite Dimension" @default.
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- W2037083588 doi "https://doi.org/10.1155/2011/919538" @default.
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