Unfaithful complex hyperbolic triangle groups, III: Arithmeticity and commensurability

Julien Paupert

doi:10.2140/pjm.2010.245.359

Unfaithful complex hyperbolic triangle groups, III: Arithmeticity and commensurability

Julien Paupert

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We prove that the so-called sporadic complex reflection triangle groups in SU(2, 1) are all nonarithmetic but one, and that they are not commensurable to Mostow or Picard lattices (with a small list of exceptions). This provides an infinite list of potential new nonarithmetic lattices in SU(2, 1).

Original language	English (US)
Pages (from-to)	359-372
Number of pages	14
Journal	Pacific Journal of Mathematics
Volume	245
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2010.245.359
State	Published - Apr 2010
Externally published	Yes

Keywords

Complex hyperbolic geometry
Complex reflection groups
Nonarithmetic lattices

ASJC Scopus subject areas

Mathematics(all)

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10.2140/pjm.2010.245.359

Cite this

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abstract = "We prove that the so-called sporadic complex reflection triangle groups in SU(2, 1) are all nonarithmetic but one, and that they are not commensurable to Mostow or Picard lattices (with a small list of exceptions). This provides an infinite list of potential new nonarithmetic lattices in SU(2, 1).",

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AB - We prove that the so-called sporadic complex reflection triangle groups in SU(2, 1) are all nonarithmetic but one, and that they are not commensurable to Mostow or Picard lattices (with a small list of exceptions). This provides an infinite list of potential new nonarithmetic lattices in SU(2, 1).

KW - Complex hyperbolic geometry

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KW - Nonarithmetic lattices

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Unfaithful complex hyperbolic triangle groups, III: Arithmeticity and commensurability

Abstract

Keywords

ASJC Scopus subject areas

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