Constructing zero divisors in the higher dimensional Cayley-Dickson algebras

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In this paper we give new methods to construct zero divisors in Aₙ =R(2ⁿ) the CayleyDickson algebras over the real numbers, for n larger than 4, and we also relate the set of zero divisors in Aₙ₊₁ with the Stiefel Manifold V₂ₙ ₋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.