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Lie point symmetry is a concept in advanced mathematics. Towards the end of the nineteenth century, Sophus Lie introduced the notion of Lie group in order to study the solutions of ordinary differential equations (ODEs). He showed the following main property: the order of an ordinary differential equation can be reduced by one if it is invariant under one-parameter Lie group of point transformations. This observation unified and extended the available integration techniques. Lie devoted the remainder of his mathematical career to developing these continuous groups that have now an impact on many areas of mathematically based sciences. The applications of Lie groups to differential systems were mainly established by Lie and Emmy Noether, and then advocated by Élie Cartan.

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rdfs:label	Lie point symmetry (en)
rdfs:comment	Lie point symmetry is a concept in advanced mathematics. Towards the end of the nineteenth century, Sophus Lie introduced the notion of Lie group in order to study the solutions of ordinary differential equations (ODEs). He showed the following main property: the order of an ordinary differential equation can be reduced by one if it is invariant under one-parameter Lie group of point transformations. This observation unified and extended the available integration techniques. Lie devoted the remainder of his mathematical career to developing these continuous groups that have now an impact on many areas of mathematically based sciences. The applications of Lie groups to differential systems were mainly established by Lie and Emmy Noether, and then advocated by Élie Cartan. (en)
dcterms:subject	Lie groups Symmetry
Wikipage page ID	26520106 (xsd:integer)
Wikipage revision ID	1086343694 (xsd:integer)
Link from a Wikipage to another Wikipage	Product rule Rotations Algebraic system Vector field Dynamical system Invariant (mathematics) Lie group Continuous symmetry Mathematics Emmy Noether Contact geometry Lie algebra Élie Cartan Algebra Algebraic variety Lie groups Symmetry Flow (mathematics) Partial differential equation Discrete symmetry Moving frame Group action (mathematics) Jacobian matrix State variable Translation (geometry) Differential form Manifold Maple (software) Sophus Lie Ordinary differential equations Lie bracket of vector fields Scaling (geometry) Smooth algebraic variety Pierre François Verhulst Differential system Lie-Bäcklund transformation Lie bracket Point transformation Continuous group Logistic growth
sameAs	Lie point symmetry Lie point symmetry Lie point symmetry Lie point symmetry
dbp:wikiPageUsesTemplate	dbt:Expand_section dbt:Reflist dbt:Lie_groups
has abstract	Lie point symmetry is a concept in advanced mathematics. Towards the end of the nineteenth century, Sophus Lie introduced the notion of Lie group in order to study the solutions of ordinary differential equations (ODEs). He showed the following main property: the order of an ordinary differential equation can be reduced by one if it is invariant under one-parameter Lie group of point transformations. This observation unified and extended the available integration techniques. Lie devoted the remainder of his mathematical career to developing these continuous groups that have now an impact on many areas of mathematically based sciences. The applications of Lie groups to differential systems were mainly established by Lie and Emmy Noether, and then advocated by Élie Cartan. Roughly speaking, a Lie point symmetry of a system is a local group of transformations that maps every solution of the system to another solution of the same system. In other words, it maps the solution set of the system to itself. Elementary examples of Lie groups are translations, rotations and scalings. The Lie symmetry theory is a well-known subject. In it are discussed continuous symmetries opposed to, for example, discrete symmetries. The literature for this theory can be found, among other places, in these notes. (en)
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is Link from a Wikipage to another Wikipage of	Lie group List of things named after Sophus Lie
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