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... > topology > algebraic topology > manifold > differentiable manifold > Lie group > homogeneous space > Kostant's convexity theorem
... > geometry > topological space > manifold > differentiable manifold > Lie group > homogeneous space > Kostant's convexity theorem
... > geometry > differential geometry > differentiable manifold > Lie group > homogeneous space > Kostant's convexity theorem
... > topology > differential topology > differentiable manifold > Lie group > homogeneous space > Kostant's convexity theorem
... > algebra > group theory > topological group > Lie group > homogeneous space > Kostant's convexity theorem
algebra > abstract algebra > algebraic structure > homogeneous space > Kostant's convexity theorem
algebra > differential algebra > Lie algebra > Kostant's convexity theorem
... > algebra > abstract algebra > algebraic structure > algebra over a field > Lie algebra > Kostant's convexity theorem

Terme préférentiel

Kostant's convexity theorem  

Définition

  • In mathematics, Kostant's convexity theorem, introduced by Bertram Kostant (1973), states that the projection of every coadjoint orbit of a connected compact Lie group into the dual of a Cartan subalgebra is a convex set. It is a special case of a more general result for symmetric spaces. Kostant's theorem is a generalization of a result of Schur (1923), Horn (1954) and Thompson (1972) for hermitian matrices. They proved that the projection onto the diagonal matrices of the space of all n by n complex self-adjoint matrices with given eigenvalues Λ = (λ1, ..., λn) is the convex polytope with vertices all permutations of the coordinates of Λ.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Kostant%27s_convexity_theorem)

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RDF/XML TURTLE JSON-LD Date de création 31/08/2023, dernière modification le 31/08/2023