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An Elliptic Non Distributive Algebra

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Abstract

In this paper we extend the results of hyperbolic scator algebra introduced in [5], to consider an elliptic product in a subset of \({\mathbb{R}^{1 + n}}\) which recovers the field of complex numbers when only one director component is present. The product of this algebra, that we call elliptic scator algebra in \({\mathbb{E}^{1 + n}}\), is associative and commutative provided that divisors of zero are excluded. However, as with the hyperbolic case, the elliptic product is not distributive over addition. We explore the geometry of this algebra by considering some interesting objects, such as spheres.

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Authors and Affiliations

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

    M. Fernández-Guasti

  2. Departamento de Matemáticas, Universidad Autónoma Metropolitana-I, 09340, México D. F., México

    Felipe Zaldívar

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  1. M. Fernández-Guasti
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  2. Felipe Zaldívar
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Correspondence to M. Fernández-Guasti.

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Fernández-Guasti, M., Zaldívar, F. An Elliptic Non Distributive Algebra. Adv. Appl. Clifford Algebras 23, 825–835 (2013). https://doi.org/10.1007/s00006-013-0406-4

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  • DOI: https://doi.org/10.1007/s00006-013-0406-4

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