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In differential geometry, the Lie derivative (/liː/ LEE), named after Sophus Lie by Władysław Ślebodziński, evaluates the change of a tensor field (including...

mathematics, the mathematician Sophus Lie (/liː/ LEE) initiated lines of study involving integration of differential equations, transformation groups, and...

In differential geometry, a Lie-algebra-valued form is a differential form with values in a Lie algebra. Such forms have important applications in the...

whole area of ordinary differential equations. However, the hope that Lie theory would unify the entire field of ordinary differential equations was not fulfilled...

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...

fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. He also made significant...

In the mathematical field of differential topology, the Lie bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector...

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other...

This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. List of curves topics...

direct product of Lie groups and p i : G → G i {\displaystyle p_{i}:G\to G_{i}} projections. Then the differentials d p i : Lie ⁡ ( G ) → Lie ⁡ ( G i ) {\displaystyle...

communications Differential GPS, in satellite navigation technology Differential interferometry in radar Differential, an extended play by The Sixth Lie Handicap...

equations. Weyl algebras and Lie algebras may be considered as belonging to differential algebra. More specifically, differential algebra refers to the theory...

study of geometry and differential equations. He also made substantial contributions to the development of algebra. Marius Sophus Lie was born on 17 December...

algebra and topology, a differential graded Lie algebra (or dg Lie algebra, or dgla) is a graded vector space with added Lie algebra and chain complex...

In differential geometry, pushforward is a linear approximation of smooth maps (formulating manifold) on tangent spaces. Suppose that φ : M → N {\displaystyle...

distinguished derivation d forms a differential algebra, and is itself a significant object of study in areas such as differential Galois theory. If A is a K-algebra...

Mackenzie, Lie Groupoids and Lie Algebroids in Differential Geometry, Cambridge U. Press, 1987. Kirill Mackenzie, General Theory of Lie Groupoids and Lie Algebroids...

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function...

{\displaystyle M} and the differential of the structure maps. Given any Lie groupoid G ⇉ M {\displaystyle G\rightrightarrows M} , there is a Lie groupoid T ∗ G ⇉...

originating however from the geometric approach of Sophus Lie to investigate symmetries of differential equations, rather than out of abstract algebra (such...