## Exploring Novel Cyclic Extensions of Hamilton’s Dual-Quaternion Algebra

**Authors:** Richard L Amoroso, Peter Rowlands, Louis H Kauffman

We make a preliminary exploratory study of higher dimensional (HD) orthogonal forms of the quaternion algebra in order to explore
putative novel Nilpotent/Idempotent/Dirac symmetry properties. Stage-1 transforms the dual quaternion algebra in a manner that
extends the standard anticommutative 3-form, i, j, k into a 5D/6D triplet. Each is a copy of the others and each is self-commutative
and believed to represent spin or different orientations of a 3-cube. The triplet represents a copy of the original that contains no new
information other than rotational perspective and maps back to the original quaternion vertex or to a second point in a line element. In
Stage-2 we attempt to break the inherent quaternionic property of algebraic closure by stereographic projection of the Argand plane
onto rotating Riemann 4-spheres. Finally, we explore the properties of various topological symmetries in order to study
anticommutative - commutative cycles in the periodic rotational motions of the quaternion algebra in additional HD dualities.

**Comments:** 11 Pages. Paper from VIII international symposium honoring mathematical physicist Jean-Pierre Vigier

**Download:** **PDF**

### Submission history

[v1] 2017-11-28 12:24:15

**Unique-IP document downloads:** 21 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*