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ARITHMETICITY OF $\mathbb {C}$-FUCHSIAN SUBGROUPS OF SOME NONARITHMETIC LATTICES

Part of: Other groups of matrices Lie groups Real and complex geometry Complex spaces with a group of automorphisms Automorphic functions

Published online by Cambridge University Press:  28 April 2023

YUEPING JIANG ,
JIEYAN WANG  and
FANG YANG
YUEPING JIANG
Affiliation:
School of Mathematics, Hunan University, Changsha, China e-mail: ypjiang@hnu.edu.cn
JIEYAN WANG
Affiliation:
School of Mathematics, Hunan University, Changsha, China e-mail: jywang@hnu.edu.cn
FANG YANG*
Affiliation:
School of Mathematics, Hunan University, Changsha, China
*
e-mail: fangyang@hnu.edu.cn
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Abstract

We study the arithmeticity of $\mathbb {C}$-Fuchsian subgroups of some nonarithmetic lattices constructed by Deraux et al. [‘New non-arithmetic complex hyperbolic lattices’, Invent. Math. 203 (2016), 681–771]. Our results give an answer to a question raised by Wells [Hybrid Subgroups of Complex Hyperbolic Isometries, Doctoral thesis, Arizona State University, 2019].

Keywords

ℂ-Fuchsian subgroupsarithmeticitynonarithmetic lattices

MSC classification

Primary: 22E40: Discrete subgroups of Lie groups
Secondary: 20H10: Fuchsian groups and their generalizations 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras 51M10: Hyperbolic and elliptic geometries (general) and generalizations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 109 , Issue 1 , February 2024 , pp. 77 - 88
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This work was supported by NSFC (grant number 12271148).

References

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