Towards a Generalized Cayley–Dickson Construction through Involutive Dimagmas

Nelson Martins-Ferreira () and Rui A. P. Perdigão ()
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Nelson Martins-Ferreira: Centre for Rapid and Sustainable Product Development, School of Technology and Management, Polytechnic Institute of Leiria, 2411-901 Leiria, Portugal
Rui A. P. Perdigão: IUC Physics of Complex Coevolutionary Systems and Fluid Dynamical Systems, Meteoceanics Institute for Complex System Science, Washington, DC 20004, USA

Mathematics, 2024, vol. 12, issue 7, 1-10

Abstract: A generalized construction procedure for algebraic number systems is hereby presented. This procedure offers an efficient representation and computation method for complex numbers, quaternions, and other algebraic structures. The construction method is then illustrated across a range of examples. In particular, the novel developments reported herein provide a generalized form of the Cayley–Dickson construction through involutive dimagmas, thereby allowing for the treatment of more general spaces other than vector spaces, which underlie the associated algebra structure.

Keywords: Cayley–Dickson; 4-tensor action; algebraic structure; magma; involutive magma (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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