Quaternions

Deformed cross products and quaternions – Introduction.

Document: Difftriad 0557v1Difftriad 0557v1 (361.98 Ko), 8 pages, 17 January 2015.

Because I am a self-made man in physics, I did not immediately recognize what certainly was an evidence for professionals.

The concept of deformed cross product is closely related to the one of differential. This document recalls this fact in taking the basis vectors as example.

It then focuses its attention on a link with the quaternionic numbers.

This link should not be too surprising, and that document should only be understood as an aperitive on that topic.

This specific link between geometry and algebra is just a peculiar illustration of a deeper connection between both branches of mathematics.

That specific link has been incorporated into another and more elaborated work than mine. The approach was able to rediscover the Einstein’s field equation in that algebraic context; see for example [01].

© Thierry PERIAT, 18 January 2021.

Bibliography:

[01] Girard, P. R.: Quaternions, Clifford Algebras and Relativistic physics.

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Last edited: 18/01/2021