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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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 ) .

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1521684026

Digital Object Identifier
doi:10.2140/agt.2018.18.957

Mathematical Reviews number (MathSciNet)
MR3773744

Zentralblatt MATH identifier
06859610

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

Keywords
quaternionic Kleinian group trace field

Citation

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. https://projecteuclid.org/euclid.agt/1521684026


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References

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