Homotopy Type Theory geometric algebra > history (changes)

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Defintion

< geometric algebra

Given a

commutative ring RR, a geometric RR-algebra is a filtered $R$-algebra AA with a ring isomorphism? j:A 0Rj:\langle A \rangle_0 \cong R such that the product of every 11-vector with itself is a 00-vector.

a:A 1[ c:A 0aa=c]\prod_{a:\langle A \rangle_1} \left[\sum_{c:\langle A \rangle_0} a \cdot a = c\right]

The 00-vectors are called scalars and 11-vectors are just called vectors

Every geometric RR-algebra is a RR-Clifford algebra.

See also

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

Last revised on June 14, 2022 at 21:17:15. See the history of this page for a list of all contributions to it.