Professional paper

Cross product on \(\mathbb{R}^{n}\), normed algebras and H–spaces

Matea Pavlek ; Prirodoslovno-matematički fakultet, Sveučilište u Zagrebu
Ozren Perše ; Prirodoslovno-matematički fakultet, Sveučilište u Zagrebu

Abstract

In this survey article, we present a construction of the cross product on \(\mathbb{R}^{n}\) , following the paper by P. F. McLoughlin, arXiv:1212.3515. We show that a naturally defined cross product exists only for n = 0, 1, 3, 7 (here \(\mathbb{R}^{0}\) denotes the zero vector space over \(\mathbb{R}\) ). We study the relationship between the cross product and Hurwitz’s theorem on the existence of normed algebras only for dimensions n = 1, 2, 4, 8, and the relationship with Adams’ theorem on continuous multiplications on spheres. Furthermore, we consider the possibilities of a generalization of the cross product on \(\mathbb{R}^{0}\) , from the function of two variables to the function of several variables.

Keywords

cross product; normed algebra; H–space

Hrčak ID:

165817

URI

https://hrcak.srce.hr/165817

Publication date:

1.8.2016.

Article data in other languages: croatian

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