Generators for the Euclidean Picard modular groups
Author:
Tiehong Zhao
Journal:
Trans. Amer. Math. Soc. 364 (2012), 3241-3263
MSC (2010):
Primary 22E40; Secondary 32M15, 32Q45
DOI:
https://doi.org/10.1090/S0002-9947-2011-05524-8
Published electronically:
November 7, 2011
MathSciNet review:
2888244
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Abstract | References | Similar Articles | Additional Information
Abstract: The goal of this article is to show that five explicitly given transformations, a rotation, two screw Heisenberg rotations, a vertical translation and an involution generate the Euclidean Picard modular groups with coefficient in the Euclidean ring of integers of a quadratic imaginary number field. We also obtain a presentation of the isotropy subgroup fixing infinity by analysis of the combinatorics of the fundamental domain in the Heisenberg group.
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Additional Information
Tiehong Zhao
Affiliation:
Institut de Mathématiques, Université Pierre et Marie Curie, 4, place Jussieu, F-75252 Paris, France
Email:
zhao@math.jussieu.fr
DOI:
https://doi.org/10.1090/S0002-9947-2011-05524-8
Received by editor(s):
July 6, 2010
Received by editor(s) in revised form:
November 25, 2010
Published electronically:
November 7, 2011
Additional Notes:
The author was supported by the China-funded Postgraduates Studying Abroad Program for Building Top University.
Article copyright:
© Copyright 2011
American Mathematical Society