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:
“A parent who from his own childhood experience is convinced of the value of fairy tales will have no difficulty in answering his childs questions; but an adult who thinks these tales are only a bunch of lies had better not try telling them; he wont be able to related them in a way which would enrich the childs life.”
—Bruno Bettelheim (20th century)
“Instead of seeing society as a collection of clearly defined interest groups, society must be reconceptualized as a complex network of groups of interacting individuals whose membership and communication patterns are seldom confined to one such group alone.”
—Diana Crane (b. 1933)