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# Rationality and the Jordan-Gatti-Viniberghi decomposition

Published:2012-12-29
Printed: Mar 2014
• Jason Levy,
Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, ON K1N 6N5
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## Abstract

We verify our earlier conjecture and use it to prove that the semisimple parts of the rational Jordan-Kac-Vinberg decompositions of a rational vector all lie in a single rational orbit.
 Keywords: reductive group, $G$-module, Jordan decomposition, orbit closure, rationality
 MSC Classifications: 20G15 - Linear algebraic groups over arbitrary fields 14L24 - Geometric invariant theory [See also 13A50]