Real adjoint orbits of special linear groups

2022/04/07 by Krishnendu Gongopadhyay, Gongopadhyay, Krishnendu, Tejbir Lohan +3
Mathematics · #Advanced Topics in Algebra #Advanced Algebra and Geometry #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2204.03624

Abstract

Let G be a Lie group with Lie algebra \mathfrakg . An element X ∈ \mathfrakg is called Ad_G-real if -X=gXg^-1 for some g ∈ G . Moreover, if -X=gXg^-1 holds for some involution g∈ G , then X is called strongly Ad_G-real. We have classified the Ad_G-real and the strongly Ad_G-real orbits in the special linear Lie algebra \mathfraksl(n,\mathbbF) for \mathbbF=ℂ or ℍ .

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