2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150847In this note, we calculate the Poincaré series of elliptic Weyl groups of type $A^{(1,1)}_1$ and $A^{(1,1) \ast}_1$ and show that they have a simple expression.9 pages, amslatex. A reference on the Bruhat-Tits buildings is added.Quantum AlgebraPoincaré series of the Weyl group of elliptic Lie algebras $A^{(1,1)}_1$ and $A^{(1,1) \ast}_1$text