Rationality and the Jordan-Gatti-Viniberghi decomposition

TL;DR

This paper proves a conjecture related to the Jordan-Gatti-Viniberghi decomposition, showing that the semisimple parts of rational decompositions are contained within a single rational orbit, advancing understanding of rational group actions.

Contribution

It verifies a conjecture and demonstrates that all semisimple parts of rational Jordan-Kac-Vinberg decompositions lie in one rational orbit.

Findings

Verification of the conjecture for the Jordan-Gatti-Viniberghi decomposition.

Semisimple parts of rational decompositions are contained in a single rational orbit.

Enhanced understanding of the structure of rational decompositions.

Abstract

We verify the conjecture of [10] 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.