Related Groups
The orthogonal groups and special orthogonal groups have a number of important subgroups, supergroups, quotient groups, and covering groups. These are listed below.
The inclusions O(n) ⊂ U(n) ⊂ Sp(n) = USp(2n) and USp(n) ⊂ U(n) ⊂ O(2n) are part of a sequence of 8 inclusions used in a geometric proof of the Bott periodicity theorem, and the corresponding quotient spaces are symmetric spaces of independent interest – for example, U(n)/O(n) is the Lagrangian Grassmannian.
Read more about this topic: Orthogonal Group
Famous quotes containing the words related and/or groups:
“The content of a thought depends on its external relations; on the way that the thought is related to the world, not on the way that it is related to other thoughts.”
—Jerry Alan Fodor (b. 1935)
“Some of the greatest and most lasting effects of genuine oratory have gone forth from secluded lecture desks into the hearts of quiet groups of students.”
—Woodrow Wilson (1856–1924)