These are things named after
Élie Cartan
Élie Joseph Cartan (; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. He ...
(9 April 1869 – 6 May 1951), a French mathematician.
Mathematics and physics
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Cartan calculus
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Cartan connection
In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also be regarded as a specialization of the general concept of a principal connection, in which the ...
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Cartan connection applications
The tetrad formalism is an approach to general relativity that generalizes the choice of basis for the tangent bundle from a coordinate basis to the less restrictive choice of a local basis, i.e. a locally defined set of four linearly independe ...
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Cartan's criterion In mathematics, Cartan's criterion gives conditions for a Lie algebra in characteristic 0 to be solvable, which implies a related criterion for the Lie algebra to be semisimple. It is based on the notion of the Killing form, a symmetric bilinear f ...
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Cartan decomposition
In mathematics, the Cartan decomposition is a decomposition of a semisimple Lie group or Lie algebra, which plays an important role in their structure theory and representation theory. It generalizes the polar decomposition or singular value deco ...
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Cartan's equivalence method
In mathematics, Cartan's equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up to a diffeomorphism. For example, if ''M'' and ''N'' are two Riemannian manifolds with metrics ' ...
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Cartan formalism (physics)
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Cartan involution
In mathematics, the Cartan decomposition is a decomposition of a semisimple Lie group or Lie algebra, which plays an important role in their structure theory and representation theory. It generalizes the polar decomposition or singular value decom ...
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Cartan's magic formula
In mathematics, the interior product (also known as interior derivative, interior multiplication, inner multiplication, inner derivative, insertion operator, contraction, or inner derivation) is a degree −1 (anti)derivation on the exterio ...
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Cartan relations
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Cartan map
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Cartan matrix In mathematics, the term Cartan matrix has three meanings. All of these are named after the French mathematician Élie Cartan
Élie Joseph Cartan (; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in ...
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Cartan pair Cartan may refer to:
* Élie Cartan (1869–1951), French mathematician who worked with Lie groups
* Henri Cartan (1904–2008), French mathematician who worked in algebraic topology, son of Élie Cartan
* Anna Cartan
Anna Cartan (15 May 1878 &n ...
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Cartan subalgebra
In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra \mathfrak of a Lie algebra \mathfrak that is self-normalising (if ,Y\in \mathfrak for all X \in \mathfrak, then Y \in \mathfrak). They were introduced by ...
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Cartan subgroup
In the theory of algebraic groups, a Cartan subgroup of a connected linear algebraic group G over a (not necessarily algebraically closed) field k is the centralizer of a maximal torus. Cartan subgroups are smooth (equivalently reduced), connec ...
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Cartan's method of moving frames
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Cartan's theorem, a name for the
closed-subgroup theorem
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Cartan's theorem, a name for the
theorem on highest weights In representation theory, a branch of mathematics, the theorem of the highest weight classifies the irreducible representations of a complex semisimple Lie algebra \mathfrak g. Theorems 9.4 and 9.5 There is a closely related theorem classifying the ...
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Cartan's theorem, a name for
Lie's third theorem In the mathematics of Lie theory, Lie's third theorem states that every finite-dimensional Lie algebra \mathfrak over the real numbers is associated to a Lie group ''G''. The theorem is part of the Lie group–Lie algebra correspondence.
Historic ...
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Einstein–Cartan theory
In theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory, is a classical theory of gravitation, one of several alternatives to general relativity. The theory was first proposed by Élie C ...
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Einstein–Cartan–Evans theory Einstein–Cartan–Evans theory or ECE theory was an attempted unified theory of physics proposed by the Welsh chemist and physicist: "ECE Theory was discovered by chemist, physicist, and mathematician, Myron Wyn Evans...". Myron Wyn Evans (May 26 ...
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Cartan–Ambrose–Hicks theorem
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Cartan–Brauer–Hua theorem
In abstract algebra, the Cartan–Brauer–Hua theorem (named after Richard Brauer, Élie Cartan, and Hua Luogeng) is a theorem pertaining to division rings. It says that given two division rings such that ''xKx''−1 is contained in '' ...
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Cartan–Dieudonné theorem
In mathematics, the Cartan–Dieudonné theorem, named after Élie Cartan and Jean Dieudonné, establishes that every orthogonal transformation in an ''n''-dimension (vector space), dimensional symmetric bilinear space can be described as the funct ...
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Cartan–Hadamard manifold
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Cartan–Hadamard theorem
In mathematics, the Cartan–Hadamard theorem is a statement in Riemannian geometry concerning the structure of complete Riemannian manifolds of non-positive sectional curvature. The theorem states that the universal cover of such a manifold is dif ...
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Cartan–Iwahori decomposition
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Cartan-Iwasawa-Malcev theorem
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Cartan–Kähler theorem In mathematics, the Cartan–Kähler theorem is a major result on the integrability conditions for differential systems, in the case of analytic functions, for differential ideals I. It is named for Élie Cartan and Erich Kähler.
Meaning
It is n ...
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Cartan–Karlhede algorithm
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Cartan–Weyl theory
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Cartan–Weyl basis
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Cartan–Killing form
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Cartan–Kuranishi prolongation theorem Given an exterior differential system defined on a manifold ''M'', the Cartan–Kuranishi prolongation theorem says that after a finite number of ''prolongations'' the system is either ''in involution'' (admits at least one 'large' integral man ...
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CAT(k) space
In mathematics, a \mathbf(k) space, where k is a real number, is a specific type of metric space. Intuitively, triangles in a \operatorname(k) space (with k0.
Let (X,d) be a geodesic metric space, i.e. a metric space for which every two points x, ...
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Maurer–Cartan form
In mathematics, the Maurer–Cartan form for a Lie group is a distinguished differential one-form on that carries the basic infinitesimal information about the structure of . It was much used by Élie Cartan as a basic ingredient of his met ...
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Newton–Cartan theory
Newton–Cartan theory (or geometrized Newtonian gravitation) is a geometrical re-formulation, as well as a generalization, of Newtonian gravity first introduced by Élie Cartan in 1923 and Kurt Friedrichs and later developed by G. Dautcourt, W. G ...
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Stokes–Cartan theorem, the generalized
fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of derivative, differentiating a function (mathematics), function (calculating its slopes, or rate of change at every point on its domain) with the concept of integral, inte ...
, proven by Cartan (in its general form), also known as
Stokes' theorem
Stokes' theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem, is a theorem in vector calculus on \R^3. Given a vector field, the theorem relates th ...
although Stokes neither formulated nor proved it.
Other
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Cartan (crater)
Cartan is a small lunar impact crater near the eastern edge of the Moon. It lies just to the west of the larger Apollonius. The rim is circular with a tiny crater along the eastern side. The interior floor is about half the diameter of the crater. ...
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Élie Cartan Prize
Note some are after
Henri Cartan
Henri Paul Cartan (; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology.
He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of c ...
, a son of É. Cartan; e.g.,
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Cartan's lemma (potential theory)
In potential theory, a branch of mathematics, Cartan's lemma, named after Henri Cartan, is a bound on the measure and complexity of the set on which a logarithmic Newtonian potential is small.
Statement of the lemma
The following statement can be ...
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Cartan seminar
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Cartan's theorems A and B
In mathematics, Cartan's theorems A and B are two results mathematical proof, proved by Henri Cartan around 1951, concerning a coherent sheaf on a Stein manifold . They are significant both as applied to Function of several complex variables, seve ...
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Cartan–Eilenberg resolution
{{DEFAULTSORT:Things named after Élie Cartan
Cartan Cartan may refer to:
* Élie Cartan (1869–1951), French mathematician who worked with Lie groups
* Henri Cartan (1904–2008), French mathematician who worked in algebraic topology, son of Élie Cartan
* Anna Cartan
Anna Cartan (15 May 1878 &n ...