Acta Mathematica Vietnamica



Trace fields of subgroups of SU(n, 1)
Juliette Genzmer



In this note, we study the field generated by the traces of subgroups of SU(n, 1). Under some hypotheses, the trace field of a group Γ⊂SU(2,1) is equal to the field generated by the coefficients of the matrices in Γ. If the group is the image of a representation of the fundamental group of a triangulated three-manifold, we can relate the trace field to a geometric invariant. For an arithmetic group of the first type in SU(n, 1), up to conjugacy, the trace field and the field of the coefficients are the same.

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