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Alternators in the Cayley-Dickson algebras
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Aaron Pixton
Published/Copyright:
August 31, 2009
Abstract
The Cayley-Dickson algebras An are an infinite sequence of (non-associative) algebras beginning with the well-known composition algebras ℝ, ℂ, ℍ, 𝕆. We completely describe all possible dimensions for the alternator Alt(a) ≔ {b ∈ An | a(ab) = (aa)b = 0} of an element a ∈ An, for n ≥ 7. This resolves a conjecture of Biss, Christensen, Dugger, and Isaksen. On the way to obtaining this result, we establish numerous results on the eigentheory of left multiplication operators in An, some of which may be of independent interest.
Received: 2007-11-13
Revised: 2008-02-14
Published Online: 2009-08-31
Published in Print: 2009-September
© de Gruyter 2009
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Articles in the same Issue
- Applications of Multivariate Asymptotics I: Boundedness of a maximal operator on
- Geodesic flow of the averaged controlled Kepler equation
- Hyperbolicity in unbounded convex domains
- Explicit connections with SU(2)-monodromy
- Eigentheory of Cayley-Dickson algebras
- Alternators in the Cayley-Dickson algebras
- Cohomological characterisation of Steiner bundles
- Sigma-cotorsion modules over valuation domains
- Affine actions on nilpotent Lie groups
- On the birational geometry of moduli spaces of pointed curves
