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Generators of a Picard modular group in two complex dimensions

Authors: Elisha Falbel, Gábor Francsics, Peter D. Lax and John R. Parker
Journal: Proc. Amer. Math. Soc. 139 (2011), 2439-2447
MSC (2010): Primary 32M05, 22E40; Secondary 32M15
Published electronically: November 30, 2010
MathSciNet review: 2784810
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Abstract: The goal of the article is to prove that four explicitly given transformations, two Heisenberg translations, a rotation and an involution generate the Picard modular group with Gaussian integers acting on the two dimensional complex hyperbolic space. The result answers positively a question raised by A. Kleinschmidt and D. Persson.

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Additional Information

Elisha Falbel
Affiliation: Institut de Mathématiques, Université Pierre et Marie Curie, 4 Place Jussieu, Paris, France

Gábor Francsics
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

Peter D. Lax
Affiliation: Courant Institute, New York University, 251 Mercer Street, New York, New York 10012-1185

John R. Parker
Affiliation: Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE, United Kingdom

Keywords: Complex hyperbolic space, Picard modular groups
Received by editor(s): October 8, 2009
Received by editor(s) in revised form: June 17, 2010
Published electronically: November 30, 2010
Additional Notes: The second author is grateful for the hospitality of the Mathematical Sciences Research Institute at Berkeley and the Rényi Mathematical Institute, Budapest.
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2010 American Mathematical Society