A Lie group structure on the space of time-dependent vector fields (Q1107884)
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scientific article; zbMATH DE number 4065969
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Lie group structure on the space of time-dependent vector fields |
scientific article; zbMATH DE number 4065969 |
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A Lie group structure on the space of time-dependent vector fields (English)
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1988
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In this note a banal relation between flows of vector fields is employed to define a natural, as regards composition of flows, non-commutative group structure on the space of time-dependent vector fields. It is shown that this group is a Lie group in the \(C_ c^{\infty}\) sense, and the adjoint action, and the exponential mapping are calculated by means of an explicit formula for the tangent to the mapping which assigns to each time-dependent vector field its flow.
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flows
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non-commutative group structure
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time-dependent vector fields
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tangent
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