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Subject Item
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Principal homogeneous space 主齐性空间 G-torsore Torsor
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。 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. 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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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, * G is a topological group, X is a topological space and the action is continuous, * G is a Lie group, X is a smooth manifold and the action is smooth, * G is an algebraic group, X is an algebraic variety and the action is regular. 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. In termini più astratti, e nel linguaggio delle categorie e dei funtori, un -torsore è un oggetto in una categoria su cui agisce un oggetto gruppo , appartenente alla stessa categoria , in modo semplicemente transitivo. Se ad esempio è la categoria degli insiemi allora X è un qualunque insieme e G è un gruppo. Se invece è la categoria degli schemi definiti sopra (ove è un campo) allora è un -schema e un -schema in gruppi. La definizione può essere generalizzata. 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。
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