Deformation of a Kac algebra by an abelian subgroup

Abstract

Some examples of quantum groups in literature arise as deformations of a locally compact group by a “dual” 2-cocycle. We make this construction in the framework of Kac algebras; we show that these deformations are still Kac algebras; using this construction, we give new quantizations of the Heisenberg group. From this point of view, we analyse the dimension 8 non-trivial example of Kac and Paljutkin, and give a new example of non-trivial dimension 12 semi-simple *-Hopf algebras (a dimension 12 Kac algebra).