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# Algèbres simples centrales de degré 5 et $E_8$

Published:2002-09-01
Printed: Sep 2002
• Philippe Gille
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## Abstract

As a consequence of a theorem of Rost-Springer, we establish that the cyclicity problem for central simple algebra of degree~5 on fields containg a fifth root of unity is equivalent to the study of anisotropic elements of order 5 in the split group of type~$E_8$.
 Keywords: algèbres simples centrales, cohomologie galoisienne
 MSC Classifications: 16S35 - Twisted and skew group rings, crossed products 12G05 - Galois cohomology [See also 14F22, 16Hxx, 16K50] 20G15 - Linear algebraic groups over arbitrary fields