Higher Order Geometric Algebras and Their Implementations Using Bott Periodicity

Abstract

Using the classification of Clifford algebras and Bott periodicity, we show how higher geometric algebras can be realized as matrices over classical low dimensional geometric algebras. This matrix representation allows us to use standard geometric algebra software packages more easily. As an example, we express the geometric algebra for conics (GAC) as a matrix over the Compass ruler algebra (CRA).Using the classification of Clifford algebras and Bott periodicity, we show how higher geometric algebras can be realized as matrices over classical low dimensional geometric algebras. This matrix representation allows us to use standard geometric algebra software packages more easily. As an example, we express the geometric algebra for conics (GAC) as a matrix over the Compass ruler algebra (CRA).