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<p>Following the work of the first and last authors [<CitationRef CitationID="CR2">2</CitationRef>], 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<sup><i>n</i></sup> 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 [<CitationRef CitationID="CR2">2</CitationRef>] does not extend to general division algebras.</p>

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On the geometry of zero sets of central quaternionic polynomials. II

  • 期刊论文

  • 发表日期：

    2025年12月11日

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  • Gil Alon,
  • Adam Chapman,
  • Elad Paran

摘要

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.