About: Principal homogeneous space

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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).An analogous definition holds in other categories, where, for example,

Attributes	Values
rdf:type	yago:WikicatLieGroups yago:WikicatTopologicalGroups yago:WikicatVectorBundles yago:Abstraction100002137 yago:Attribute100024264 yago:Collection107951464 yago:Group100031264 yago:Package108008017 yago:Space100028651 yago:WikicatAlgebraicHomogeneousSpaces
rdfs:label	Torsor (ca) G-torsore (it) Principal homogeneous space (en) 主齐性空间 (zh)
rdfs:comment	数学上，对于群 G的主齐性空间，或者叫 G-旋子（英文：torsor），是一个集合 X， G在其上自由并可递地作用。也即，X是G的齐性空间，满足每个点的定点子群都是平凡群。在其它范畴中有类似的定义，其中 * G是一拓扑群， X是一拓扑空间，而作用是连续的， * G是一李群， X是一光滑流形而作用是光滑的， * G是一代数群， X是一代数簇而作用是的。 (zh) 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).An analogous definition holds in other categories, where, for example, (en) In matematica, un -torsore (anche detto spazio omogeneo principale), fissato un gruppo , è un G-insieme su quale agisce liberamente e transitivamente. In questa definizione concreta, sia che appartengono alla categoria degli insiemi e in quanto oggetti di questa sono dunque insiemi. (it)
dcterms:subject	Group theory Topological groups Vector bundles Lie groups Diophantine geometry Algebraic homogeneous spaces
Wikipage page ID	363441 (xsd:integer)
Wikipage revision ID	1041826435 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Cartesian product Basis (linear algebra) Algebraic group Algebraically closed field Homogeneous space Vector space Lie group Group theory Mathematics General linear group Genus (mathematics) Tangent bundle Classifying space Elliptic curve Linear algebra Smooth function Topological groups Vector bundles Topological group Galois cohomology Heap (mathematics) K-frame Local analysis Affine space Algebraic variety American Mathematical Society Lie groups Fiber bundle Flag (geometry) Diophantine geometry Number field Number theory Frame bundle Isomorphism Quadratic form Projective linear group Rational point Regular function Regular polytope Group (mathematics) Group action (mathematics) Group cohomology Abelian variety Algebraic homogeneous spaces Cohomology Ternary operation Stabilizer subgroup Diophantine equation Automorphism group Manifold Continuous (topology) Group object Identity (mathematics) Algebraically closed Orthogonal group Category (mathematics) Category theory Scheme (mathematics) Selmer group Smooth manifold Nonabelian group Principal bundle Tate-Shafarevich group Parallelizable Topological space Severi–Brauer variety Stiefel manifold Orthonormal bases Base point Descent (category theory) Differential manifold
Link from a Wikipage to an external page	https://archive.org/details/torsorsrationalp0000skor http://math.ucr.edu/home/baez/torsors.html
sameAs	Principal homogeneous space

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