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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.53 no.2 Bogotá July/Dec. 2019 Epub Mar 20, 2020
Artículos originales
On a family of groups generated by parabolic matrices
Sobre una familia de grupos generados por matrices parabólicas
1 Institut für Mathematik Technische Universität Berlin D-19623 Berlin, Germany e-mail:
2 Escuela de Matemáticas Universidad Nacional de Colombia, sede Medellín facultad de ciencias calle 59a n.63-20 Medellín, Colombia e-mail: mmtoro@unal.edu.co
We study various aspects of the family of groups generated by the parabolic matrices A(t
1
ζ),. .. , A(t
m
ζ) where A(z) = (
) and by the elliptic matrix (
). The elements of the matrices W in such groups can be computed by a recursion formula. These groups are special cases of the generalized parametrized modular groups introduced in [16].
We study the sets {z : tr W(z) Є [-2, +2]} [13] and their critical points and geometry, furthermore some finite index subgroups and the discretness of subgroups.
Key words and phrases. modular group; parametrized modular group; singular set; discrete groups; Chebyshev polynomials
Estudiamos algunos aspectos de la familia de grupos generados por matrices parabólicas A(t
1
ζ),...,A(t
m
ζ) donde A(z) = (
) y por la matriz elíptica (
). Los elementos de las matrices W en tales grupos se pueden calcular mediante una formula de recurrencia. Estos grupos son casos especiales de la generalizacion del grupo modular parametrizado estudiado en [16].
Estudiamos los conjuntos {z : tr W(z) Є [-2, +2]} [13] y sus puntos críticos y geometría, así como tambien algunos subgrupos de índice finito y la discreticidad de tales subgrupos.
Palabras y frases clave. grupo modular; grupo modular parametrizado; conjunto singular; grupos discretos; polinomios de Chebyshev
Acknowledgment.
The authors want to thank the referee for his suggestions.
References
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Received: May 2019; Accepted: September 2019
Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons BY
