Abstract
We present an eight-dimensional even sub-algebra of the -dimensional associative Clifford algebra and show that its eight-dimensional elements denoted as and respect the norm relation thus forming an octonion-like but associative normed division algebra, where the norms are calculated using the fundamental geometric product instead of the usual scalar product. The corresponding 7-sphere has a topology that differs from that of octonionic 7-sphere.
Notes
1 The conformal space we are considering is an in-homogeneous version of the space usually studied in Conformal Geometric Algebra [Citation5]. It can be viewed as an 8-dimensional subspace of the 32-dimensional representation space postulated in Conformal Geometric Algebra. The larger representation space results from a homogeneous freedom of the origin within which does not concern us in this article.