The quaternionic projective space is the space of right (or left) quaternion lines through the origin in , hence the space of equivalence classes of (n+1)-tuples of quaternions excluding zero, under the equivalence relation given by right (or left) multiplication with non-zero quaternions
As any Grassmannian, quaternion projective space is canonically a coset space, in this case of the quaternion unitary group by the central product group Sp(n).Sp(1):
By the coset space-realization (1), quaternion projective space is naturally a quaternion-Kähler manifold which is also a symmetric space. As such it is an example of a Wolf space.
See also
M-theory on the 8-manifold HP2, hence on a quaternion-Kähler manifold of dimension 8 with holonomy Sp(2).Sp(1), is considered in
and argued to be dual to M-theory on G2-manifolds in three different ways, which in turn is argued to lead to a a possible proof of confinement in the resulting 4d effective field theory (see there for more).
Last revised on February 7, 2021 at 04:59:15. See the history of this page for a list of all contributions to it.