Homotopy Type Theory geometric algebra > history (Rev #4)

Defintion

Given a commutative ring $R$, a $R$-geometric algebra is a graded $R$-module and an $R$-algebra $A$ with canonical ring homomorphism $i:R \to A$ with an isomorphism? $j:\langle A \rangle_0 \cong R$ and a quadratic form $(-)^2:\langle A \rangle_1 \to R$.

Every $R$-geometric algebra is a $R$-Clifford algebra.

See also

• Clifford algebra
• algebra (ring theory)
• real geometric algebra
• graded module

References

• G. Aragón, J.L. Aragón, M.A. Rodríguez (1997), Clifford Algebras and Geometric Algebra, Advances in Applied Clifford Algebras Vol. 7 No. 2, pg 91–102, doi:10.1007/BF03041220, S2CID:120860757