Cartan's theorem may refer to several mathematical results by Élie Cartan: Closed-subgroup theorem, 1930, that any closed subgroup of a Lie group is a...

In mathematics, Cartan's theorems A and B are two results proved by Henri Cartan around 1951, concerning a coherent sheaf F on a Stein manifold X. They...

generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement about...

In mathematics, the Cartan–Dieudonné theorem, named after Élie Cartan and Jean Dieudonné, establishes that every orthogonal transformation in an n-dimensional...

In mathematics, the Cartan–Hadamard theorem is a statement in Riemannian geometry concerning the structure of complete Riemannian manifolds of non-positive...

In mathematics, the closed-subgroup theorem (sometimes referred to as Cartan's theorem) is a theorem in the theory of Lie groups. It states that if H is...

In mathematics, the Cartan–Kähler theorem is a major result on the integrability conditions for differential systems, in the case of analytic functions...

cohomology and coherent sheaves and proved two powerful results, Cartan's theorems A and B. Since the 50's he became more interested in algebraic topology...

was impressed by Cartan's unusual abilities. He recommended Cartan to participate in a contest for a scholarship in a lycée. Cartan prepared for the contest...

In mathematics, the Cartan–Ambrose–Hicks theorem is a theorem of Riemannian geometry, according to which the Riemannian metric is locally determined by...

In abstract algebra, the Cartan–Brauer–Hua theorem (named after Richard Brauer, Élie Cartan, and Hua Luogeng) is a theorem pertaining to division rings...

Trichotomy theorem (finite groups) Walter theorem (finite groups) Z* theorem (finite groups) ZJ theorem (finite groups) Cartan's theorem (Lie group)...

literature of the second half of 20th century) Cartan's or the Cartan-Lie theorem as it was proved by Élie Cartan. Sophus Lie had previously proved the infinitesimal...

Killing, later refined and generalized by Élie Cartan, led to classification of semisimple Lie algebras, Cartan's theory of symmetric spaces, and Hermann Weyl's...

Weyl's work and Cartan's theorem gives a survey of the whole representation theory of compact groups G. That is, by the Peter–Weyl theorem the irreducible...

Kuranishi provided a proof of Cartan's conjecture. This theorem is used in infinite-dimensional Lie theory. Cartan-Kähler theorem Bryant, Robert L.; Chern...

several important results such as the Ahlfors's Five Islands theorem, Cartan's theorem on holomorphic curves omitting hyperplanes, Hayman's result that...

The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded...

following sequence of results. Complex analysis was revolutionized by Cartan's theorems A and B in 1953. These results say that if F {\displaystyle {\mathcal...

H^{2}(X,\mathbb {Z} )\longrightarrow H^{2}(X,{\mathcal {O}}_{X})} Now Cartan's theorem B shows that H 1 ( X , O X ) = H 2 ( X , O X ) = 0 {\displaystyle H^{1}(X...

Cartan matrix Cartan pair Cartan subalgebra Cartan subgroup Cartan's method of moving frames Cartan's theorem, a name for the closed-subgroup theorem...

also, (i) is used to prove Cartan's theorems A and B. In the case of one variable complex functions, Mittag-Leffler's theorem was able to create a global...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

manifolds are similar to affine complex algebraic varieties is that Cartan's theorems A and B hold for Stein manifolds. Examples of Stein manifolds include...

2 ( M , Z ) = 0. {\displaystyle H^{2}(M,\mathbb {Z} )=0.} Cartan's theorems A and B Cartan, Henri (1950). "Idéaux et modules de fonctions analytiques...

groups G such as Lie groups (H. Cartan's theorem).[clarification needed] As was shown by the Bott periodicity theorem, the homotopy groups of BG are also...

In mathematics, the Borel–Weil–Bott theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can...

{g}}=[{\mathfrak {g}},{\mathfrak {g}}]} is nilpotent. Lie's theorem also establishes one direction in Cartan's criterion for solvability: If V is a finite-dimensional...

G. In particular, if G is a Lie group, then H is a Lie subgroup by Cartan's theorem. Hence G / H is a smooth manifold and so X carries a unique smooth...

construction theorem is a theorem which constructs a fiber bundle from a given base space, fiber and a suitable set of transition functions. The theorem also...