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

Kim, Sungwoon; Kim, Joonhyung

doi:10.2140/agt.2018.18.957

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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

DOI: 10.2140/agt.2018.18.957

Abstract

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 $U (2, 1)$ .

Keywords

quaternionic Kleinian group, trace field

Mathematical Subject Classification 2010

Primary: 22E40, 30F40, 57S30

References

Publication

Received: 19 January 2017

Revised: 30 August 2017

Accepted: 17 September 2017

Published: 12 March 2018

Authors

Sungwoon Kim
Department of Mathematics Jeju National University Jeju South Korea

Joonhyung Kim
Department of Mathematics Education Jeonju University Jeonju South Korea

Volume 18, issue 2 (2018)