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:
“Well, most men have bound their eyes with one or another handkerchief, and attached themselves to some of these communities of opinion. This conformity makes them not false in a few particulars, authors of a few lies, but false in all particulars. Their every truth is not quite true. Their two is not the real two, their four not the real four; so that every word they say chagrins us and we know not where to set them right.”
—Ralph Waldo Emerson (1803–1882)
“Specialization is a feature of every complex organization, be it social or natural, a school system, garden, book, or mammalian body.”
—Catharine R. Stimpson (b. 1936)
“Youth is not a question of years: one is young or old from birth.”
—Natalie Clifford Barney (1876–1972)