On the geometry of zero sets of central quaternionic polynomials II
Rings and Algebras
2025-01-14 v2
Abstract
Following the work of the first and last authors [2], we further analyze the structure of a zero set of a left ideal in the ring of central polynomials over the quaternion algebra H. We describe the "algebraic hull" of a point in H^n and prove it is a product of spheres. Using this description we give a new proof to a conjecture of Gori, Sarfatti and Vlacci. We also show that the main result of [2] does not extend to general division algebras.
Keywords
Cite
@article{arxiv.2408.08246,
title = {On the geometry of zero sets of central quaternionic polynomials II},
author = {Gil Alon and Adam Chapman and Elad Paran},
journal= {arXiv preprint arXiv:2408.08246},
year = {2025}
}