Quantum groups and deformations of preprojective algebras

Let Γ be a quiver containing finite cyclic blocks and Πλ(Γ) be the deformed preprojective algebra of Γ. It is proved that a suitable quotient uq of Πλ(Γ) for an appropriate vector λ is a finite-dimensional quantum group. Some properties of uq are also obtained. An isomorphism as Hopf algebras is given between uq and a restricted quantum group .