Conversely, symmetric spaces with compact isotropy group are Riemannian symmetric spaces, although not necessarily in a unique way.
2.
To avoid discussing the finite groups appearing, the lists present the Lie algebra of the isotropy group rather than the isotropy group itself.
3.
To avoid discussing the finite groups appearing, the lists present the Lie algebra of the isotropy group rather than the isotropy group itself.
4.
Since the corresponding eigenvalue must be a complex number of modulus 1, this gives the U ( 1 ) factor of the isotropy group.
5.
From the form of the general coordinate basis expression given above, it is apparent that the stress energy tensor has precisely the same isotropy group as the null vector field \ vec { k }.
6.
Lorentz transformations play the same role in Minkowski geometry ( the Lorentz group forms the " isotropy group " of the self-isometries of the spacetime ) which are played by rotations in euclidean geometry.
7.
The other part of the isotropy group is parametrized by the unitary matrices on the orthogonal complement of | \ psi \ rangle, which is isomorphic to U ( " n "-1 ).
8.
The Radon transform, for example, is the orbital integral that results by taking " G " to be the Euclidean isometry group and " K " the isotropy group of a hyperplane.
9.
Here E _ { VCYC } ( G ) denotes the classifying space of the group " G " with respect to the family of virtually cyclic subgroups, i . e . a " G "-CW-complex whose isotropy groups are virtually cyclic and for any virtually cyclic subgroup of " G " the fixed point set is contractible.
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