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Essential dimension of Albert algebras

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<mark>Journal publication date</mark>2014
<mark>Journal</mark>Bulletin of the London Mathematical Society
Publication StatusPublished
Early online date20/06/14
<mark>Original language</mark>English


This paper shows that the number of independent parameters required to describe an Albert algebra up to isomorphism is at most seven. In other words, the essential dimension of the split group of type F 4 over a field of characteristic not 2 or 3 satisfies ed(F 4 )≤7 . This is achieved by reducing the structural group from the full 52-dimensional automorphism group to a subgroup of dimension 10, and exhibiting an eighteen-dimensional generically free linear representation that remains generically free once projectivized.