A note on trace fields of complex hyperbolic groups
Heleno Cunha
Universidade Federal de Minas Gerais, Belo Horizonte, BrazilNikolay Gusevskii
Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
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Abstract
We show that if is an irreducible subgroup of SU(2,1), then contains a loxodromic element . If has eigenvalues , , , we prove that is conjugate in SU(2,1) to a subgroup of SU, where is the field generated by the trace field of and . It follows from this that if is an irreducible subgroup of SU(2,1) such that the trace field is real, then is conjugate in SU(2,1) to a subgroup of SO(2,1). As a geometric application of the above, we get that if is an irreducible discrete subgroup of PU(2,1), then is an -Fuchsian subgroup of PU(2,1) if and only if the invariant trace field of is real.
Cite this article
Heleno Cunha, Nikolay Gusevskii, A note on trace fields of complex hyperbolic groups. Groups Geom. Dyn. 8 (2014), no. 2, pp. 355–374
DOI 10.4171/GGD/229