Title: Octonions
Author: Angeliki Koutsoukou-Argyraki
Submission date: 2018-09-14
Abstract: We develop the basic theory of Octonions, including various identities and properties of the octonions and of the octonionic product, a description of 7D isometries and representations of orthogonal transformations. To this end we first develop the theory of the vector cross product in 7 dimensions. The development of the theory of Octonions is inspired by that of the theory of Quaternions by Lawrence Paulson. However, we do not work within the type class real_algebra_1 because the octonionic product is not associative.
  author  = {Angeliki Koutsoukou-Argyraki},
  title   = {Octonions},
  journal = {Archive of Formal Proofs},
  month   = sep,
  year    = 2018,
  note    = {\url{https://isa-afp.org/entries/Octonions.html},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.