Pseudoquaternion geometry
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.
quaternion and pseudo-quaternion geometry
biquaternion and pseudo-biquaternion operators
scientific article; zbMATH DE number 1930632