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geometry > algebraic geometry > Diophantine geometry > principal homogeneous space
number > number theory > Diophantine geometry > principal homogeneous space
... > topology > algebraic topology > manifold > differentiable manifold > Lie group > homogeneous space > principal homogeneous space
... > geometry > topological space > manifold > differentiable manifold > Lie group > homogeneous space > principal homogeneous space
... > geometry > differential geometry > differentiable manifold > Lie group > homogeneous space > principal homogeneous space
... > topology > differential topology > differentiable manifold > Lie group > homogeneous space > principal homogeneous space
... > algebra > group theory > topological group > Lie group > homogeneous space > principal homogeneous space
algebra > abstract algebra > algebraic structure > homogeneous space > principal homogeneous space
topology > differential topology > vector bundle > principal homogeneous space

Preferred term

principal homogeneous space  

Definition

  • In mathematics, a principal homogeneous space, or torsor, for a group G is a homogeneous space X for G in which the stabilizer subgroup of every point is trivial. Equivalently, a principal homogeneous space for a group G is a non-empty set X on which G acts freely and transitively (meaning that, for any x, y in X, there exists a unique g in G such that x·g = y, where · denotes the (right) action of G on X).
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Principal_homogeneous_space)

Broader concept

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URI

http://data.loterre.fr/ark:/67375/PSR-PN64B2Q9-R

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RDF/XML TURTLE JSON-LD Created 8/23/23, last modified 8/23/23