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A Non-distributive Extension of Complex Numbers to Higher Dimensions

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An Erratum to this article was published on 12 October 2015

Abstract

The additive representation of elliptic scator algebra, a finite 1 + n dimensional non distributive algebra, is extended to a multiplicative or polar representation in a subset of \({\mathbb{R}^{1+n}}\). The addition and product operations are stated in both representations and their consistency is proven. The product is shown to be always commutative, having neutral and inverse for all elements except zero, where both representations exist. Associativity is not always fulfilled due to the existence of zero products. There are n copies of the complex plane having the real axis in common, embedded in 1 + n dimensional elliptic scator algebra.

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  1. Lab. de Óptica Cuántica, Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, 09340, México D.F, Ap. postal. 55-534, Mexico

    M. Fernández-Guasti

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  1. M. Fernández-Guasti
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Correspondence to M. Fernández-Guasti.

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Fernández-Guasti, M. A Non-distributive Extension of Complex Numbers to Higher Dimensions. Adv. Appl. Clifford Algebras 25, 829–849 (2015). https://doi.org/10.1007/s00006-015-0539-8

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  • DOI: https://doi.org/10.1007/s00006-015-0539-8

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