Examples: Real and Complex Clifford Algebras
The most important Clifford algebras are those over real and complex vector spaces equipped with nondegenerate quadratic forms.
It turns out that every one of the algebras Cℓp,q(R) and Cℓn(C) are isomorphic to A or A⊕A, where A is a full matrix ring with entries from R, C, or H. For a complete classification of these algebras see classification of Clifford algebras.
Read more about this topic: Clifford Algebra
Famous quotes containing the words real, complex and/or clifford:
“We are beginning a new era in our government. I cannot too strongly urge the necessity of a rigid economy and an inflexible determination not to enlarge the income beyond the real necessities of the government.”
—Andrew Jackson (1767–1845)
“I have met charming people, lots who would be charming if they hadn’t got a complex about the British and everyone has pleasant and cheerful manners and I like most of the American voices. On the other hand I don’t believe they have any God and their hats are frightful. On balance I prefer the Arabs.”
—Freya Stark (1893–1993)
“How many inner resources one needs to tolerate a life of leisure without fatigue”
—Natalie Clifford Barney (1876–1972)