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:
“The real sin against life is to abuse and destroy beauty, even one’s own—even more, one’s own, for that has been put in our care and we are responsible for its well-being.”
—Katherine Anne Porter (1890–1980)
“We must open our eyes and see that modern civilization has become so complex and the lives of civilized men so interwoven with the lives of other men in other countries as to make it impossible to be in this world and out of it.”
—Franklin D. Roosevelt (1882–1945)
“How many inner resources one needs to tolerate a life of leisure without fatigue”
—Natalie Clifford Barney (1876–1972)