Torsor

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 . 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.

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