Algebraic & Geometric Topology

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

Sungwoon Kim and Joonhyung Kim

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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 ) .

Article information

Algebr. Geom. Topol., Volume 18, Number 2 (2018), 957-974.

Received: 19 January 2017
Revised: 30 August 2017
Accepted: 17 September 2017
First available in Project Euclid: 22 March 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 30F40: Kleinian groups [See also 20H10] 57S30: Discontinuous groups of transformations

quaternionic Kleinian group trace field


Kim, Sungwoon; Kim, Joonhyung. A characterization of quaternionic Kleinian groups in dimension $2$ with complex trace fields. Algebr. Geom. Topol. 18 (2018), no. 2, 957--974. doi:10.2140/agt.2018.18.957.

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