2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145847We construct a one parameter deformation of the group of $2\times 2$ upper triangular matrices with determinant 1 using the twisting construction. An interesting feature of this new example of a locally compact quantum group is that the Haar measure is deformed in a non-trivial way. Also, we give a complete description of the dual $\cs$-algebra and the dual comultiplication.Operator Algebras46L65; 46L52text