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Multiplicative Representation of a Hyperbolic non Distributive Algebra

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Abstract

The multiplicative or polar representation of hyperbolic scator algebra in 1 + n dimensions is introduced. The transformations between additive and multiplicative representations are presented. The addition and product operations are consistently defined in either representation using additive or multiplicative variables. The product is shown to produce a rotation and scaling for equal director components and solely a scaling in the orthogonal components.

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Authors and Affiliations

  1. Laboratorio de Óptica Cuántica, Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México, D. F., México

    Manuel Fernández-Guasti

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

    Felipe Zaldívar

Authors
  1. Manuel Fernández-Guasti
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  2. Felipe Zaldívar
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Correspondence to Manuel Fernández-Guasti.

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Fernández-Guasti, M., Zaldívar, F. Multiplicative Representation of a Hyperbolic non Distributive Algebra. Adv. Appl. Clifford Algebras 24, 661–674 (2014). https://doi.org/10.1007/s00006-014-0454-4

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  • DOI: https://doi.org/10.1007/s00006-014-0454-4

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