Balanced toral elements of exceptional Lie algebras

Floriana Amicone (Manchester)

Frank Adams 1,

Let \(g\) be a Lie algebra defined over a field of char \(p>0\), and let \(G\) be a connected algebraic group with Lie algebra \(g\). A toral element of \(g\) is called balanced if its adjoint action decomposes \(g\) as a direct sum of eigenspaces all of the same dimension, except for the centraliser.
 
For exceptional Lie algebras it is possible to classify \(G\)-conjugacy classes of balanced toral elements by relying on the description of nilpotent orbits and applying combinatorial arguments.
As a result, one obtains the classification of \(G\)-classes of balanced automorphisms of order \(p\) of exceptional Lie algebras in characteristic \(0\).
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