A locally compact quantum group of triangular matrices.

Pierre Fima (1) , Leonid Vainerman (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Mots clés: Quantum groups; twisting; Rieffel's deformations

Domaines: Algèbres d'opérateurs [math.OA]

Pierre Fima, Leonid Vainerman. A locally compact quantum group of triangular matrices.. 2008. ⟨hal-00204132⟩