Abstract
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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Acknowledgments
We thank N. Bergeron, E. Falbel, B. McReynolds, J. Paupert, E. Ramos, and P. Will for many fruitful discussions.
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Genzmer, J. TRACE FIELDS OF SUBGROUPS OF SU(n, 1). Acta Math Vietnam 39, 313–323 (2014). https://doi.org/10.1007/s40306-014-0063-2
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DOI: https://doi.org/10.1007/s40306-014-0063-2