Clifford Algebras

Projective Metric Geometry and Clifford Algebras

“…The latter set can be made into a group in a natural way and as such it acts on the initial projective metric space P(V , Q). In Theorems 5.4, 5.5 and 5.6 we carry out a detailed study of this group action and its kernel, thereby extending previous work of Gunn [19,20], Jurk [32], Klawitter and Hagemann [36], Klawitter [35], Schröder [49] and others. Since the details are somewhat involved, an alternative point of view is adopted in Tables 1, 2 and 3.…”

“…From (8), the even subalgebras of Cl(V , Q) and Cl(V , Q, c ) coincide (as algebras), as do their odd parts (as vector spaces). Our quest for going over to projective space on Cl(V , Q) comes from an observation resulting from (35): for all homogeneous elements p, q ∈ Cl(V , Q), we have F (pq) = F (p c q) despite the fact that their products pq and p c q need not coincide. From (11), Theorems 6.2, 6.3 and Remark 6.4 we readily obtain: Corollary 6.6.…”

Projective metric geometry and Clifford algebras

“…The latter set can be made into a group in a natural way and as such it acts on the initial projective metric space P(V, Q). In Theorems 5.4, 5.5 and 5.6 we carry out a detailed study of this group action and its kernel, thereby extending previous work of C. Gunn [19], [20], R. Jurk [32], M. Hagemann and D. Klawitter [36], [35], E. M. Schröder [49] and others. Since the details are somewhat involved, an alternative point of view is adopted in Tables 1-3.…”

“…From (8), the even subalgebras of Cl(V, Q) and Cl(V, Q, ⊙ c ) coincide (as algebras), as do their odd parts (as vector spaces). Our quest for going over to the projective space on Cl(V, Q) comes from an observation resulting from (35): for all homogeneous elements p, q ∈ Cl(V, Q), we have F(pq) = F(p⊙ c q) despite the fact that their products pq and p ⊙ c q need not coincide. From (11), Theorem 6.2, Theorem 6.3 and Remark 6.4 we readily obtain: Corollary 6.6.…”