Involution and commutator length for complex hyperbolic isometries

TL;DR

This paper investigates how complex hyperbolic isometries can be decomposed into involutions, establishing bounds on involution length and commutator length for various groups.

Contribution

It proves 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.

Findings

PU(2,1) has involution length 4.

PU(2,1) has commutator length 1.

For all n ≥ 3, PU(n,1) has involution length ≤ 8.

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 $n \geqslant 3$ PU($n$,1) has involution length at most 8.