Homotopy Type Theory
geometric algebra > history (Rev #6, changes)
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Defintion
< geometric algebra
Given a commutative ring R R , a geometric R R -algebra is a filtered $R$-algebra A A with a ring isomorphism? j : ⟨ A ⟩ 0 ≅ R j:\langle A \rangle_0 \cong R such that the product of every 1 1 -vector with itself is a 0 0 -vector.
∏ a : ⟨ A ⟩ 1 [ ∑ c : ⟨ A ⟩ 0 a ⋅ a = c ] \prod_{a:\langle A \rangle_1} \left[\sum_{c:\langle A \rangle_0} a \cdot a = c\right]
The 0 0 -vectors are called scalars and 1 1 -vectors are just called vectors
Every geometric R R -algebra is a R R -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
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