Involution and Commutator Length for Complex Hyperbolic Isometries

Abstract

We study decompositions of complex hyperbolic isometries as products of involutions. We show that $PU(2,1)$ has involution length 4 and commutator length 1 and that, for all $n⩾3$, $PU(n,1)$ has involution length at most 8.