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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,

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  • Principal homogeneous space
  • G-torsore
  • 主齐性空间
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  • 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。
  • 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,
  • 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.
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