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

Autor(es)

de Oliveira Benedito, Cintya Wink ^[1] ; Palazzo, Jr., Reginaldo ^[1] ; Interlando, J. Carmelo ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Commun, BR-13083852 Sao Paulo - Brazil

^[2] San Diego State Univ, Dept Math & Stat, San Diego, CA 92182 - USA

• Tipo de documento: Artigo Científico
• Fonte: Journal of Pure and Applied Algebra; v. 220, n. 5, p. 1902-1923, MAY 2016.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 07/56052-8 - Teoria da informação e códigos
• Beneficiário: Sueli Irene Rodrigues Costa
• Modalidade de apoio: Auxílio à Pesquisa - Temático