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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

An algorithm to construct arithmetic Fuchsian groups derived from quaternion algebras and the corresponding hyperbolic lattices

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Author(s):
de Oliveira Benedito, Cintya Wink [1] ; Palazzo, Jr., Reginaldo [1] ; Interlando, J. Carmelo [2]
Total Authors: 3
Affiliation:
[1] Univ Estadual Campinas, Dept Commun, BR-13083852 Sao Paulo - Brazil
[2] San Diego State Univ, Dept Math & Stat, San Diego, CA 92182 - USA
Total Affiliations: 2
Document type: Journal article
Source: Journal of Pure and Applied Algebra; v. 220, n. 5, p. 1902-1923, MAY 2016.
Web of Science Citations: 0
Abstract

The aim of this paper is to propose an algorithm to construct arithmetic Fuchsian groups derived from quaternion algebras and quaternion orders which will lead to the construction of hyperbolic lattices. To achieve this goal a necessary condition for obtaining arithmetic Fuchsian groups Gamma(p) from a tessellation [p, q] whose regular hyperbolic polygon P-p generates an oriented surface with genus g >= 2 is established. This necessary condition is called Fermat condition due to its identification with the Fermat primes. It is also shown an isomorphism between arithmetic Fuchsian groups derived from different edge-pairings sets of the regular fundamental region associated with the tessellation [4g, 4g] for g = 2(n), 3.2(n), 5.2(n), and 3.5.2(n), and the tessellation [4g + 2, 2g + 1] for g = 2. One set uses the normal form whereas the other one uses diametrically opposite edge-pairings. All these transformations are hyperbolic and so result in an oriented compact Riemann surface. (C) 2015 Elsevier B.V. All rights reserved. (AU)