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.
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