DEFORMATION OF A KAC ALGEBRA BY AN ABELIAN SUBGROUP

Some examples of quantum groups in literature arise as deformations of a locally compact group by a ''dual'' 2-cocycle. We make this constru ction in the framework of Kac algebras; we show that these deformation s are still Kac algebras; using this construction, we give new quantiz ations of the Heisenberg group. From this point of view, we analyse th e dimension 8 non-trivial example of Kac and Paljutkin, and give a new example of non-trivial dimension 12 semi-simple -Hopf algebras (a di mension 12 Kac algebra).