منابع مشابه
Analysis of a Picard modular group.
Our main goal is to analyze the geometric and spectral properties of the Picard modular group with Gaussian integer entries acting on the two-dimensional complex hyperbolic space.
متن کاملElliptic points of the Picard modular group
We explicitly compute the elliptic points and isotropy groups for the action of the Picard modular group over the Gaussian integers on 2-dimensional complex hyperbolic space.
متن کاملGenerators of a Picard Modular Group in Two Complex Dimensions
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.
متن کاملThe Geometry of the Eisenstein-picard Modular Group
The Eisenstein-Picard modular group PU(2, 1;Z[ω]) is defined to be the subgroup of PU(2, 1) whose entries lie in the ring Z[ω], where ω is a cube root of unity. This group acts isometrically and properly discontinuously on H C , that is, on the unit ball in C2 with the Bergman metric. We construct a fundamental domain for the action of PU(2, 1;Z[ω]) on H2 C , which is a 4-simplex with one ideal...
متن کاملThe geometry of the Gauss-Picard modular group
We give a construction of a fundamental domain for the group PU(2, 1,Z[i]). That is the group of holomorphic isometries of complex hyperbolic space with coefficients in the Gaussian ring of integers Z[i]. We obtain from that construction a presentation of that lattice and relate it, in particular, to lattices constructed by Mostow.
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 2006
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.0603075103