A locally compact quantum group of triangular matrices
  We 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. 
Pierre Fima (LM-Besan\c{c}on), Leonid Vainerman (LMNO)