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...

{\displaystyle k} -frames) are still homogeneous spaces for the orthogonal group, but not principal homogeneous spaces: any k {\displaystyle k} -frame can...

manifold V n ( F n ) {\displaystyle V_{n}(\mathbb {F} ^{n})} is a principal homogeneous space for the corresponding classical group. When k is strictly less...

importance to Cartan and his contemporaries was how to identify a principal homogeneous space of G. That is, a manifold P identical to the group G, but without...

(orthonormal k-frames) are still homogeneous spaces for the orthogonal group, but not principal homogeneous spaces: any k-frame can be taken to any other...

specified fibre is a principal homogeneous space for the left action of the group on itself, yielding the associated principal bundle. If, in addition...

that each fiber is a principal homogeneous space. The bundle is often specified along with the group by referring to it as a principal G {\displaystyle G}...

is that an affine space is a principal homogeneous space for the action of the additive group of a vector space. Homogeneous spaces are, by definition...

mentioning quarks at all. It is a nonlinear sigma model with the principal homogeneous space of a Lie group G {\displaystyle G} as its target manifold. When...

yield the Bott periodicity theorems. The specific spaces are, (for groups, the principal homogeneous space is also listed): Bott's original proof (Bott 1959)...