Normalizers of congruence groups in SL2(R) and automorphisms of lattices

Shaul Zemel

doi:https://doi.org/10.1142/S1793042117500701

Normalizers of congruence groups in SL₂(R) and automorphisms of lattices

Shaul Zemel

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

We determine the normalizer in SL₂(R) of several families of congruence subgroups of SL₂(Z). In addition, we show how these tools can be used to evaluate the groups of automorphisms and the discriminant kernels of a large family of isotropic lattices of signature (2,1).

Original language	English
Pages (from-to)	1275-1300
Number of pages	26
Journal	International Journal of Number Theory
Volume	13
Issue number	5
DOIs	https://doi.org/10.1142/S1793042117500701
State	Published - 1 Jun 2017

Keywords

Congruence subgroups
automorphisms of lattices
generalized Atkin-Lehner involutions
normalizers

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Access to Document

https://doi.org/10.1142/S1793042117500701

Cite this

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abstract = "We determine the normalizer in SL2(R) of several families of congruence subgroups of SL2(Z). In addition, we show how these tools can be used to evaluate the groups of automorphisms and the discriminant kernels of a large family of isotropic lattices of signature (2,1).",

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AB - We determine the normalizer in SL2(R) of several families of congruence subgroups of SL2(Z). In addition, we show how these tools can be used to evaluate the groups of automorphisms and the discriminant kernels of a large family of isotropic lattices of signature (2,1).

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KW - automorphisms of lattices

KW - generalized Atkin-Lehner involutions

KW - normalizers

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JO - International Journal of Number Theory

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