Projective Algebra $\Lambda_{n}$

Oliver Conradt, Goetheanum, Section for Mathematics and Astronomy, Switzerland

Projective algebra is defined as a double algebra $\Lambda_{n}(+,\ ,\wedge,\vee)$ together with an equivalence and a position relation. There is no metric present in pure projective geometry. The same holds for the $2^{n}$ dimensional algebra $\Lambda_{n}(+,\ ,\wedge,\vee)$. Geometric concepts such as primitive geometric forms, the principle of duality, cross ratio and projective mappings are introduced. Projective mappings $\Phi$ preserve the $\wedge$ and the $\vee$ product; one of both by definition, the second up to the factor $\det\Phi$. Binary indices for the basic elements of the projective algebra facilitate computations. The transition from projective to geometric Clifford algebra will be given.