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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Generators of a Picard modular group in two complex dimensions
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by Elisha Falbel, Gábor Francsics, Peter D. Lax and John R. Parker PDF
Proc. Amer. Math. Soc. 139 (2011), 2439-2447 Request permission

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.
References
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Additional Information
  • Elisha Falbel
  • Affiliation: Institut de Mathématiques, Université Pierre et Marie Curie, 4 Place Jussieu, Paris, France
  • Email: falbel@math.jussieu.fr
  • Gábor Francsics
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • Email: francsics@math.msu.edu
  • Peter D. Lax
  • Affiliation: Courant Institute, New York University, 251 Mercer Street, New York, New York 10012-1185
  • Email: lax@courant.nyu.edu
  • John R. Parker
  • Affiliation: Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE, United Kingdom
  • MR Author ID: 319072
  • ORCID: 0000-0003-0513-3980
  • Email: j.r.parker@durham.ac.uk
  • 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
  • © Copyright 2010 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 2439-2447
  • MSC (2010): Primary 32M05, 22E40; Secondary 32M15
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10653-6
  • MathSciNet review: 2784810