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Essential dimension of Albert algebras

Research output: Contribution to journalJournal article

Published

Journal publication date2014
JournalBulletin of the London Mathematical Society
Early online date20/06/14
Original languageEnglish

Abstract

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.