Pseudoquaternion geometry
type: Item
instance of: scholarly article
title: Pseudoquaternion geometry
zbMATH Open document ID: 1039.53082
DOI: 10.1023/A:1014475315820
publication date: 2002-01-01T00:00:00Z
review text: The author introduces two new types of transformations in the quaternionic vector space \(\mathbb{H}^n\), generalizing or specializing (linear) quaternionic mappings. Recall first that the quaternion left vector space \(\mathbb{H}^n\) admits a natural complex structure and a natural real structure. In the complex context, the author defines a \textit{pseudo-quaternionic linear transformation} to be a complex linear transformation mapping left quaternion subspaces to left quaternionic subspaces. He classifies these completely and extends his results to pseudo-quaternionic diffeomorphisms of \(\mathbb{H}^n\) and to other (admissible) complex structures on \(\mathbb{H}^n\). In the real setting, he defines \textit{pseudo-biquaternionic operators} as additive and continuous operators on \(\mathbb{H}^n\) which take left (quaternionic) lines to left lines and right ones to right ones. Again, a full description of such operators is given.
reviewed by: Eric Boeckx
Mathematics Subject Classification ID: 53C56
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 53C26
zbMATH DE Number: 1930632
zbMATH Keywords: quaternion and pseudo-quaternion geometry
zbMATH Keywords: biquaternion and pseudo-biquaternion operators
author: Vładimir I. Arnold
MaRDI profile type: Publication
full work available at URL: a:1014475315820
OpenAlex ID: W4236173630
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1930632