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arXiv · 1908.02942

The cyclicity problem for Albert algebras

Maneesh Thakur
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Abstract

In this paper we address the celebrated Albert problem for exceptional Jordan algebras (i.e. Albert algebras): Does every Albert division algebra contain a cubic cyclic subfield? We prove that for any Albert division algebra $A$ over a field $k$ of arbitrary characteristic, there is a suitable isotope that contains a cubic cyclic subfield. It follows from this that for any Albert division algebra $A$ over a field $k$, the structure group $\text{\bf Str}(A)$ always contains a subgroup of type $^3D_4$ defined over $k$.

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Maneesh Thakur. 2019-08-08. The cyclicity problem for Albert algebras. https://arxiv.org/abs/1908.02942

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