Z. Reichstein,
Higher trace forms and essential dimension in central simple algebras,
Archiv der Mathematik, 88, no. 1 (2007), 12--18. Posted March 2006.
Abstract:
Let A/K be a finite-dimensional central simple algebra and
Tr be the reduced trace function in A. We show that the essential dimension
of A is captured by the r-linear trace form
(a_1, ..., a_r) -> Tr(a_1 ... a_r), for any r >= 3.