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On a family of groups generated by parabolic matrices
Sobre una familia de grupos generados por matrices parabólicas
DOI:
https://doi.org/10.15446/recolma.v53n2.85541Parole chiave:
modular group, parametrized modular group, singular set, discrete groups, Chebyshev polynomials (en)grupo modular, grupo modular parametrizado, conjunto singular, grupos discretos, polinomios de Chebyshev (es)
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0 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.
0 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.
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