title: Coincidence lattices in the hyperbolic plane.
abstract: The problem of coincidences of lattices in the space R(p,q), with p + q = 2, is analyzed using Clifford algebra. We show that, as in R(n), any coincidence isometry can be decomposed as a product of at most two reflections by vectors of the lattice. Bases and coincidence indices are constructed explicitly for several interesting lattices. Our procedure is metric-independent and, in particular, the hyperbolic plane is obtained when p = q = 1. Additionally, we provide a proof of the Cartan-Dieudonné theorem for R(p,q), with p + q = 2, that includes an algorithm to decompose an orthogonal transformation into a product of reflections.
authors.affiliation: Departamento de Matemáticas, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, Edificio 9. 07300 México DF, México.
authors.forename: M A
authors.initials: MA
authors.lastname: Rodríguez-Andrade
authors.forename: G
authors.initials: G
authors.lastname: Aragón-González
authors.forename: J L
authors.initials: JL
authors.lastname: Aragón
authors.forename: A
authors.initials: A
authors.lastname: Gómez-Rodríguez