Reversible complex hyperbolic isometries (Q1938589)

Let \(\operatorname{PU}(n,1)\) denote the isometry group of the \(n\)-dimensional complex hyperbolic space. An isometry g is called reversible if g is conjugate to its inverse in \(\operatorname{PU}(n,1)\). If g can be expressed as a product of two involutions, it is called strongly reversible. In this paper, the authors obtain a complete classification of the reversible and strongly reversible elements in \(\operatorname U(n,1)\), in \(\operatorname{SU}(n,1)\) or in \(\operatorname{PU}(n,1)\).