2025/12/15 by Shoot Koebisu, Koebisu, Shoot
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2512.13002
openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/31
We study zero-divisors in the 16-dimensional sedenion algebra from the viewpoint of the determinant of left multiplication. We show that this determinant admits a canonical factorization into the square of a quartic polynomial, obtained via a G2-invariant reduction to a quaternionic normal form and an explicit block computation. The quartic factor recovers the classical characterization of left zero-divisors in terms of the imaginary components. After normalization, the resulting zero-divisor manifold is identified with the Stiefel manifold V2(ℝ7). We also analyze a 3-dimensional purely imaginary slice, on which the quartic reduces to a simple quadratic form. This yields a concrete geometric model of the zero-divisor locus as a quadratic cone in the slice.