Quadratic Spinor Polynomials with Infinitely Many Factorizations
Rings and Algebras
2024-02-23 v1
Abstract
Spinor polynomials are polynomials with coefficients in the even sub-algebra of conformal geometric algebra whose norm polynomial is real. They describe rational conformal motions. Factorizations of spinor polynomial corresponds to the decomposition of the rational motion into elementary motions. Generic spinor polynomials allow for a finite number of factorizations. We present two examples of quadratic spinor polynomials that admit infinitely many factorizations. One of them, the circular translation, is well-known. The other one has only been introduced recently but in a different context. We not only compute all factorizations of these conformal motions but also interpret them geometrically.
Cite
@article{arxiv.2402.14347,
title = {Quadratic Spinor Polynomials with Infinitely Many Factorizations},
author = {Zijia Li and Hans-Peter Schröcker and Johannes Siegele and Daren A. Thimm},
journal= {arXiv preprint arXiv:2402.14347},
year = {2024}
}