Poisson--Lie contractions and quantum (1+1) groups

Abstract

A Poisson--Hopf algebra of smooth functions on the (1+1) Cayley--Klein groups is constructed by using a classical $r$--matrix which is invariant under contraction. The quantization of this algebra for the Euclidean, Galilei and Poincaré cases is developed, and their duals are also computed. Contractions on these quantum groups are studied.

7 pages