Volume 18, issue 2 (2018)

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A characterization of quaternionic Kleinian groups in dimension $2$ with complex trace fields

Sungwoon Kim and Joonhyung Kim

Algebraic & Geometric Topology 18 (2018) 957–974
Abstract

Let $G$ be a nonelementary discrete subgroup of $Sp\left(2,1\right)$. We show that if the sum of diagonal entries of each element of $G$ is a complex number, then $G$ is conjugate to a subgroup of $U\left(2,1\right)$.

Keywords
quaternionic Kleinian group, trace field
Mathematical Subject Classification 2010
Primary: 22E40, 30F40, 57S30