Homotopy Type Theory Clifford algebra > history (changes)

A $R$-pre-Clifford algebra homomorphism between two $R$-pre-Clifford algebras $A$ and $B$ is an $R$-algebra homomorphism $f:A \to B$ such that the quadratic form is preserved

The $R$-Clifford algebra $Cl(R, q)$ is the initial object in the category of $R$-pre-Clifford algebras and $R$-pre-Clifford algebra homomorphisms.

Suppose an $n$-dimensional $R$-Clifford algebra $A$ has a basis vector function $e:U(n) \to A$, where

is the type of natural numbers less than $n$, such that for all $i:U(n)$, $q(e_i) = 1$. Then $q$ is the standard diagonal form and $A$ is usually written as $Cl_n(R)$.

See also

• algebra (ring theory)
• geometric algebra