Examples
For example, the root system of A2 consists of the vertices of a regular hexagon centered at the origin. The Weyl group of this root system is a subgroup of index two of the dihedral group of order 12. It is isomorphic to S3, the symmetric group generated by the three reflections on the main diagonals of the hexagon.
Read more about this topic: Weyl Group
Famous quotes containing the word examples:
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)