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Eight-dimensional Octonion-like but Associative Normed Division Algebra

Research paper by Joy Christian

Indexed on: 02 Sep '20Published on: 12 Aug '19Published in: arXiv - Mathematics - General Mathematics



Abstract

We present an eight-dimensional even sub-algebra of the 2^4 = 16-dimensional associative Clifford algebra Cl(4,0) and show that its eight-dimensional elements denoted as X and Y respect the norm relation ||XY|| = ||X|| ||Y||, 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.