Constructing zero divisors in the higher dimensional Cayley-Dickson algebras

2005/12/22 by Guillermo Moreno, Moreno, Guillermo · 1 citation
Computer Science · Mathematics · #17A99 #Algebraic Topology (math.AT) #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods for differential equations #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.math/0512517

openalex publication_date 2005/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give new methods to construct zero divisors in A_n =R^(2ⁿ) the Cayley_Dickson algebras over the real numbers, for n larger than 4, and we also relate the set of zero divisors in A_n+1 with the Stiefel Manifold V_{2ⁿ -1,2} for n>3. We also introduce the notion of "Spectrum" (of a no zero double pure element) wich synthesize the information regarding the structure of the linear operators left and right multiplication by the element. We use this as a main technical tool to construct the zero divisors.

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Related

• The zero divisors of the Cayley-Dickson algebras over the real numbers
• Large annihilators in Cayley-Dickson algebras
• Structure of the Cayley-Dickson algebras
• Monomorphisms between Cayley-Dickson Algebras
• Framework-Independent Zero Divisor Patterns in Higher-Dimensional Cayley-Dickson Algebras: Discovery and Verification of The Canonical Six