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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

Let G be a nonelementary discrete subgroup of Sp(2,1). 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(2,1).

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quaternionic Kleinian group, trace field
Mathematical Subject Classification 2010
Primary: 22E40, 30F40, 57S30
Received: 19 January 2017
Revised: 30 August 2017
Accepted: 17 September 2017
Published: 12 March 2018
Sungwoon Kim
Department of Mathematics
Jeju National University
South Korea
Joonhyung Kim
Department of Mathematics Education
Jeonju University
South Korea