2025/12/22 by François Digne, Jean Michel, Digne, François +1
Mathematics · #math.GR
paper · pdf · doi:10.48550/arxiv.2512.19164
Let \bG be a connected reductive algebraic group over an algebraically closed field, and let s∈\bG be a semisimple element. We show that the centraliser of s is the semidirect product of its identity component by its group of components. We then look at the case where \bG is defined over an algebraic closure of a finite field \Fq, and F is an endomorphism such that some power is a Frobenius endomorphism attached to an \Fq-structure on \bG. We show that if the centraliser of s is F-stable we have a semidirect product decomposition of its F-fixed points.