Sobre una familia de grupos generados por matrices parabólicas

• Pommerenke, Christian ^[1] ; Toro, Margarita ^[2]
  1. [1] Technical University of Berlin

     Technical University of Berlin

     Berlin, Stadt, Alemania

     
  2. [2] Universidad Nacional de Colombia

     Universidad Nacional de Colombia

     Colombia

     
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 53, Nº. 2, 2019, págs. 221-236
• Idioma: español
• DOI: 10.15446/recolma.v53n2.85541
• Títulos paralelos:
  • On a family of groups generated by parabolic matrices
• Enlaces
  • Texto completo
• Resumen
  • español

    Estudiamos algunos aspectos de la familia de grupos generados por matrices parabólicas A(t1 ζ), ... , A(tm ζ) donde A(z) = ( 1 z0 1 ) y por la matriz elíptica ( 0 -1  1 0 ). Los elementos de las matrices W en tales grupos se pueden calcular mediante una fórmula de recurrencia. Estos grupos son casos especiales de la generalización del grupo modular parametrizado estudiado en [16].Estudiamos los conjuntos {z : tr W(z) ∈ [-2; +2]} [13] y sus puntos críticos y geometría, así como también algunos subgrupos de índice finito y la discreticidad de tales subgrupos.

  • English

    We study various aspects of the family of groups generated by the parabolic matrices A(t1 ζ), ... , A(tm ζ) where A(z) = ( 1 z0 1 ) and by the elliptic matrix ( 0 -1  1 0 ). 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) ∈ [-2; +2]} [13] and their critical points and geometry, furthermore some finite index subgroups and the discretness of subgroups.

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