Reversibility and real adjoint orbits of linear maps (Q6191235)

Summary: We extend the classical results on the classification of the reversible elements of the group \(\mathrm{GL}(n, \mathbb{C})\) (and \(\mathrm{GL}(n, \mathbb{R})\)) to \(\mathrm{GL}(n, \mathbb{H})\) using an infinitesimal version of the classical reversibility, namely adjoint reality in the Lie algebra set-up. We also provide a new proof of such a classification for the general linear groups over \(\mathbb{R}\) and \(\mathbb{C}\). Further, we classify the real adjoint orbits in the Lie algebra \(\mathfrak{gl}(n, \mathbb{D})\) for \(\mathbb{D = \mathbb{R}}\), \(\mathbb{C}\) or \(\mathbb{H}\). For the entire collection see [Zbl 1519.57002].