A note on trace fields of complex hyperbolic groups

Heleno Cunha, Nikolay Gusevskii

We show that if $\Gamma$ is an irreducible subgroup of $\mathrm{SU}(2,1)$, then $\Gamma$ contains a loxodromic element $A$. If $A$ has eigenvalues ${\lambda }_1=\lambda e^{i\phi },$ ${\lambda }_2=e^{-2i\phi }$, $λ_3 = λ^{-…