Reversible complex hyperbolic isometries☆

Abstract

Let PU(n,1)denote the isometry group of then-dimensional com-plex hyperbolic space HnC. An isometrygis calledreversibleifgisconjugate tog−1in PU(n,1).Ifgcan be expressed as a product oftwo involutions, it is calledstrongly reversible. We classify reversibleand strongly reversible elements in PU(n,1).Wealsoinvestigatereversibility and strong reversibility in SU(n,1)