A quantum group at roots of unity

We construct a quantum deformation of corresponding to the deformation parameter , where N is an even natural number. Hopf *-algebra, Hilbert space and C*-algebra levels are considered. The C*-algebra A, which may be interpreted as the algebra of all continuous functions on the group vanishing at infinity, is generated by five elements α, β, γ, δ and det−1 satisfying certain commutation relations completed by hermiticity conditions. The group structure is encoded by a comultiplication Φ ϵ Mor (A, A ⊗ A) acting on generators in the standard way. On the Hopf algebra level our deformation corresponds to a one-parameter family of the standard two-parameter deformations .