TY - JOUR
T1 - On the geometry of zero sets of central quaternionic polynomials. II
AU - Alon, Gil
AU - Chapman, Adam
AU - Paran, Elad
N1 - Publisher Copyright:
© The Hebrew University of Jerusalem 2025.
PY - 2025
Y1 - 2025
N2 - 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 ℍn 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.
AB - 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 ℍn 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.
UR - https://www.scopus.com/pages/publications/105024957838
U2 - 10.1007/s11856-025-2879-y
DO - 10.1007/s11856-025-2879-y
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AN - SCOPUS:105024957838
SN - 0021-2172
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
ER -