Homotopy Type Theory Clifford algebra > history (Rev #1)

Defintion

Given a commutative ring $R$ , a $R$ -pre-Clifford algebra is an $R$ -algebra $A$ with a canonical injection $\iota: R \to A$ and a quadratic form $q:A \to R$ such that

\prod_{a:A} a \cdot a = \iota(q(a))

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

\prod_{a:A} q_A(a) = q_B(f(a))

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

Homotopy Type Theory Clifford algebra > history (Rev #1)

Defintion

See also