Geometry of integral binary hermitian forms

We generalize Conwayʼs approach to integral binary quadratic forms to study integral binary hermitian forms over quadratic imaginary extensions of Q. We show that every indefinite anisotropic form determines a plane (“ocean”) in Mendozaʼs spine associated to the corresponding Bianchi group in the hy...

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Bibliographic Details
Published in:Journal of algebra 2012-06, Vol.360, p.1-20
Main Authors: Bestvina, Mladen, Savin, Gordan
Format: Article
Language:English
Subjects:
Hermitian forms
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Summary:We generalize Conwayʼs approach to integral binary quadratic forms to study integral binary hermitian forms over quadratic imaginary extensions of Q. We show that every indefinite anisotropic form determines a plane (“ocean”) in Mendozaʼs spine associated to the corresponding Bianchi group in the hyperbolic 3-space. The ocean can be used to compute the group of integral transformations preserving the hermitian form.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2012.03.017