Mark L. MacDonald: Essential dimension of Albert algebras

Submission: 2013, Nov 26

This paper shows that the number of independent parameters required to describe an Albert algebra up to isomorphism is at most 7. 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 18-dimenional generically free linear representation which remains generically free once projectivized.

2010 Mathematics Subject Classification:

Keywords and Phrases: Essential dimension, Albert algebras, generically free representations

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