Application
Quaternion algebras are applied in number theory, particularly to quadratic forms. They are concrete structures that generate the elements of order two in the Brauer group of F. (For some fields, including algebraic number fields, every element of index 2 in its Brauer group is represented by a quaternion algebra. A theorem of Merkurjev says the elements of index 2 in the Brauer group of any field are represented by a tensor product of quaternion algebras.) In particular, over p-adic fields the construction of quaternion algebras can be viewed as the quadratic Hilbert symbol of local class field theory.
Read more about this topic: Quaternion Algebra
Famous quotes containing the word application:
“The application requisite to the duties of the office I hold [governor of Virginia] is so excessive, and the execution of them after all so imperfect, that I have determined to retire from it at the close of the present campaign.”
—Thomas Jefferson (1743–1826)
“There are very few things impossible in themselves; and we do not want means to conquer difficulties so much as application and resolution in the use of means.”
—François, Duc De La Rochefoucauld (1613–1680)
“My business is stanching blood and feeding fainting men; my post the open field between the bullet and the hospital. I sometimes discuss the application of a compress or a wisp of hay under a broken limb, but not the bearing and merits of a political movement. I make gruel—not speeches; I write letters home for wounded soldiers, not political addresses.”
—Clara Barton (1821–1912)