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In this paper we prove some trace identities in  SL (3,C) and  SU (2,1) groups. We also present the merits on how to parametrise pair of pants via traces and cross-ratio. Finally, we compute traces of matrices that are generated by complex reflections in complex triangle groups.

Traces in <i>SL</i>(3,C) and <i>SU</i>(2,1) Groups